Maximal Factorization of Operators Acting in Kothe-Bochner Spaces

[EN] Using some representation results for Kothe-Bochner spaces of vector valued functions by means of vector measures, we analyze the maximal extension for some classes of linear operators acting in these spaces. A factorization result is provided, and a specific representation of the biggest vector valued function space to which the operator can be extended is given. Thus, we present a generalization of the optimal domain theorem for some types of operators on Banach function spaces involving domination inequalities and compactness. In particular, we show that an operator acting in Bochner spaces of p-integrable functions for any 1First author is supported by Grant MTM2011-23164 of the Ministerio de Economia y Competitividad (Spain). Second author is supported by Grant 284110 of CONACyT (Mexico). Fourth author is supported by Grant MTM2016-77054-C2-1-P of the Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigaciones (Spain) and FEDER.Calabuig, JM.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, EA. (2021). Maximal Factorization of Operators Acting in Kothe-Bochner Spaces. Journal of Geometric Analysis. 31(1):560-578. https://doi.org/10.1007/s12220-019-00290-4S56057831

On the continuous Cesàro operator in certain function spaces

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"Various properties of the (continuous) Cesàro operator C, acting on Banach and Fréchet spaces of continuous functions and L p-spaces, are investigated. For instance, the spectrum and point spectrum of C are completely determined and a study of certain dynamics of C is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of C acting in the various spaces is identified.The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesàro operator in certain function spaces. Positivity. 19:659-679. https://doi.org/10.1007/s11117-014-0321-5S65967919Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: $$C_0$$ C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)Galaz Fontes, F., Solís, F.J.: Iterating the Cesàro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesàro–Hardy. Misc. Mat. 57, 103–117 (2013)González, M., León-Saavedra, F.: Cyclic behaviour of the Cesàro operator on $$L_2(0,+\infty )$$ L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Leibowitz, G.M.: Spectra of finite range Cesàro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)Leibowitz, G.M.: The Cesàro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesàro type operators. Math. Nachr. 282, 764–773 (2009)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: Terzioğlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980

Kothe dual of Banach lattices generated by vector measures

We study the Kothe dual spaces of Banach function lattices generated by abstract methods having roots in the theory of interpolation spaces. We apply these results to Banach spaces of integrable functions with respect to Banach space valued countably additive vector measures. As an application we derive a description of the Banach dual of a large class of these spaces, including Orlicz spaces of integrable functions with respect to vector measuresThe first author was supported by the Foundation for Polish Science (FNP). The second author was supported by the Ministerio de Economia y Competitividad (Spain) under Grant #MTM2012-36740-C02-02.Mastylo, M.; Sánchez Pérez, EA. (2014). Kothe dual of Banach lattices generated by vector measures. Monatshefte fur Mathematik. 173(4):541-557. https://doi.org/10.1007/s00605-013-0560-8S5415571734Aronszajn, N., Gagliardo, E.: Interpolation spaces and interpolation methods. Ann. Mat. Pura. Appl. 68, 51–118 (1965)Bartle, R.G., Dunford, N., Schwartz, J.: Weak compactness and vector measures. Canad. J. Math. 7, 289–305 (1955)Brudnyi, Yu.A., Krugljak, N.Ya.: Interpolation functors and interpolation spaces $$I$$ I . North-Holland, Amsterdam (1991)Curbera, G.P.: Operators into $$L^1$$ L 1 of a vector measure and applications to Banach lattices. Math. Ann. 293, 317–330 (1992)Curbera, G.P., Ricker, W.J.: The Fatou property in $$p$$ p -convex Banach lattices. J. Math. Anal. Appl. 328, 287–294 (2007)Delgado, O.: Banach function subspaces of $$L^1$$ L 1 of a vector measure and related Orlicz spaces. Indag. Math. 15(4), 485–495 (2004)Diestel, J., Jr., Uhl, J.J.: Vector measures, Amer. Math. Soc. Surveys 15, Providence, R.I. (1977)Fernández, A., Mayoral, F., Naranjo, F., Sánchez-Pérez, E.A.: Spaces of $$p$$ p -integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Ferrando, I., Rodríguez, J.: The weak topology on $$L_p$$ L p of a vector measure. Topol. Appl. 155, 1439–1444 (2008)Ferrando, I., Sánchez Pérez, E.A.: Tensor product representation of the (pre)dual of the $$L_p$$ L p -space of a vector measure. J. Aust. Math. Soc. 87, 211–225 (2009)Galaz-Fontes, F.: The dual space of $$L^p$$ L p of a vector measure. Positivity 14(4), 715–729 (2010)Kamińska, A.: Indices, convexity and concavity in Musielak-Orlicz spaces, dedicated to Julian Musielak. Funct. Approx. Comment. Math. 26, 67–84 (1998)Kantorovich, L.V., Akilov, G.P.: Functional analysis, 2nd edn. Pergamon Press, New York (1982)Krein, S.G., Petunin, Yu.I., Semenov, E.M.: Interpolation of linear operators. In: Translations of mathematical monographs, 54. American Mathematical Society, Providence, R.I., (1982)Lewis, D.R.: Integration with respect to vector measures. Pacific. J. Math. 33, 157–165 (1970)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 583–599 (1973)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Lozanovskii, G.Ya.: On some Banach lattices, (Russian). Sibirsk. Mat. Z. 10, 419–430 (1969)Musielak, J.: Orlicz spaces and modular spaces. In: Lecture Notes in Math. 1034, Springer-Verlag, Berlin (1983)Okada, S.: The dual space of $$L^1(\mu )$$ L 1 ( μ ) of a vector measure $$\mu$$ μ . J. Math. Anal. Appl. 177, 583–599 (1993)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces, operator theory. Adv. Appl., vol. 180, Birkhäuser, Basel (2008)Rao, M.M., Zen, Z.D.: Applications of Orlicz spaces. Marcel Dekker, Inc., New York (2002)Rivera, M.J.: Orlicz spaces of integrable functions with respect to vector-valued measures. Rocky Mt. J. Math. 38(2), 619–637 (2008)Sánchez Pérez, E.A.: Compactness arguments for spaces of $$p$$ p -integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces. Ill. J. Math. 45(3), 907–923 (2001)Sánchez Pérez, E.A.: Vector measure duality and tensor product representation of $$L_p$$ L p spaces of vector measures. Proc. Amer. Math. Soc. 132, 3319–3326 (2004)Zaanen, A.C.: Integration. North Holland, Amsterdam (1967

Biographies and Careers throughout Academic Life

The book draws on the 2007 Changing Academic Profession international survey in order to document the personal characteristics, career trajectories, sense of identity/commitment and job satisfaction of academics in 14 countries with different levels of economic and social development and different higher education systems. With nearly 26,000 academics surveyed in 19 countries (of which 14 are reporting their results in this volume), the empirical basis of the book is the most up-to-date and far-reaching in the area. With major changes taking place both in the local and global contexts of higher education and in the working conditions within individual universities, as exemplified by increasing managerialism and performance-based funding, it is important to consider the impact of these changes on the profiles and working lives of the academic profession across different countries. But it is also important to look at the ways in which the faculty’s changing profile impacts on the organisation and management of universities and on the delivery of their central functions. Although not always obvious in the short-term, academic work and its conditions attract, incorporate and promote different types of individuals who, in turn, exert considerable influence on the nature of academic work, higher education institutions and, potentially, society. As faculty members are central to the teaching, research and service enterprise activities of higher education, it is important to understand their personal characteristics, career trajectories, sense of identity and commitment, and job satisfaction. These are central for understanding the academic profession in general and, in particular, the factors affecting their involvement and productivity in the work of their institutions. These are a complex result of a mixture of contextual factors (e.g. the status and regulatory framework of the higher education system, the features and atmosphere of the particular institution) and personal factors (e.g. gender, educational attainment, family background, attitudes to work and broader social values).This book examines the different situations facing the academic profession in individual countries and provides comparative studies of country differences

Fourier transform and convolutions on L(p) of a vector measure on a compact Hausdorff abelian group

The final publication is available at Springer via http://dx.doi.org/10.1007/s00041-012-9252-3"Let ν be a countably additive vector measure defined on the Borel subsets of a compact Hausdorff abelian group G. In this paper we define and study a vector valued Fourier transform and a vector valued convolution for functions which are (weakly) integrable with respect to ν. A form of the Riemann Lebesgue Lemma and a Uniqueness Theorem are established in this context. In order to study the vector valued convolution we discuss the invariance under reflection in G of these spaces of integrable functions. Finally we present a Young’s type inequality in this setting and several relevant examples, namely related with the vector measure associated to different important classical operators coming from Harmonic Analysis.J.M. Calabuig was supported by Ministerio de Economia y Competitividad and FEDER (project MTM2008-04594) and MEC "Jose Castillejo 2008". E. A. Sanchez Perez was supported by Ministerio de Economia y Competitividad and FEDER (project MTM2012-36740-c02-02). J.M. Calabuig and E. A. Sanchez Perez were also supported by "Ayuda para Estancias de PDI de la UPV en centros de investigacion de prestigio" (PAID-00-11).Calabuig Rodriguez, JM.; Galaz-Fontes, F.; Navarrete, EM.; Sánchez Pérez, EA. (2013). Fourier transform and convolutions on L(p) of a vector measure on a compact Hausdorff abelian group. Journal of Fourier Analysis and Applications. 19(2):312-332. doi:10.1007/s00041-012-9252-3S312332192Blasco, O., Calabuig, J.M.: Fourier analysis with respect to bilinear maps. Acta Math. Sin. Engl. Ser. 25(4), 519–530 (2009)del Campo, R., Fernández, A., Ferrando, I., Mayoral, F., Naranjo, F.: Multiplication operators on spaces on integrable functions with respect to a vector measure. J. Math. Anal. Appl. 343(1), 514–524 (2008)Delgado, O., Miana, P.J.: Algebra structure for L p of a vector measure. J. Math. Anal. Appl. 358(2), 355–363 (2009)Diestel, J., Uhl, J.J.: Vector Measures. Math. Surveys, vol. 15. Amer. Math. Soc., Providence (1977)Ferrando, I., Galaz-Fontes, F.: Multiplication operators on vector measure Orlicz spaces. Indag. Math. 20(1), 57–71 (2009)Fernández, A., Mayoral, F., Naranjo, F., Sánchez Pérez, E.A.: Complex interpolation of spaces of integrable functions with respect to a vector measure. Collect. Math. 61(3), 241–252 (2010)Katznelson, Y.: An Introduction to Harmonic Analysis. Cambridge University Press, Cambridge (2004)Mockenhaupt, G., Ricker, W.J.: Optimal extension of the Hausdorff-Young inequality. J. Reine Angew. Math. 620, 195–211 (2008)Pap, E.: Handbook of Measure Theory. North-Holland/Elsevier, Amsterdam (2002)Talagrand, M.: Pettis Integral and Measure Theory. Memoirs of the AMS, vol. 307 (1984)Okada, S., Ricker, W., Sánchez Pérez, E.A.: Optimal Domain and Integral Extension of Operators acting in Function Spaces. Oper. Theory Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Rudin, W.: Fourier Analysis on Groups. Interscience, New York (1967)Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. North Holland, Amsterdam (1971

A Portrait of the Changing Academic Profession in the Netherlands

This chapter describes, based on the Netherlands’ CAP (Changing Academic Profession) survey, the personal backgrounds, attitudes toward careers and career trajectories, the views on scholarship and job satisfaction of academics in Netherlands. The survey considered a representative sample of the staff in all academic ranks that were involved in teaching and/or research tasks at (research) universities and at Universities of Applied Sciences (UAS). According to the survey results the proportion of female academics has increased, along with the acceptance of English as the common language in the academia. Traditional tasks and academic values have survived major policy reforms, contributing to maintain satisfaction levels. Compared to their international colleagues, Dutch academics stand out on various aspects of the profession such as the strong notion of scholarship focused on original and basic research

Key Challenges to the Academic Profession

This publication comprises the papers presented to a workshop held on 5-6 September 2006 in Kassel, Germany. It was initiated by the Regional Scientific Committee for Europe and North America of the UNESCO Forum for Higher Education, Research and Knowledge. - Gedruckte Ausg. im Verlag Jenior, Kassel, erschienen