Mean ergodic multiplication operators on weighted spaces of continuous functions

[EN] Multiplication operators on weighted Banach spaces and locally convex spaces of continuous functions have been thoroughly studied. In this note, we characterize when continuous multiplication operators on a weighted Banach space and on a weighted inductive limit of Banach spaces of continuous functions are power bounded, mean ergodic or uniformly mean ergodic. The behaviour of the operator on weighted inductive limits depends on the properties of the defining sequence of weights and it differs from the Banach space case.The research of Bonet was partially supported by Project Prometeo/2017/102 of the Generalitat Valenciana. The authors authors were also partially supported by MINECO Project MTM2016-76647-P. Rodriguez also thanks the support of the Grant PAID-01-16 of the Universitat Politecnica de Valencia.Bonet Solves, JA.; Jorda Mora, E.; Rodríguez-Arenas, A. (2018). Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterranean Journal of Mathematics. 15(3):1:108-11:108. https://doi.org/10.1007/s00009-018-1150-8S1:10811:108153Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988)Bierstedt, K.D.: A survey of some results and open problems in weighted inductive limits and projective description for spaces of holomorphic functions. Bull. Soc. Roy. Sci. Liège 70(4–6), 167–182 (2001)Bierstedt, K.D., Bonet, J.: Some recent results on VC(X). In: Advances in the theory of Fréchet spaces (Istanbul, 1988), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 287, pp. 181–194. Kluwer Acad. Publ., Dordrecht (1989)Bierstedt, K.D., Bonet, J.: Completeness of the (LB)-spaces VC(X). Arch. Math. (Basel) 56(3), 281–285 (1991)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat 97(2), 159–188 (2003)Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272(1), 107–160 (1982)Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces. In: Functional analysis, holomorphy and approximation theory, Rio de Janeiro, pp. 27–91 (1980)Bonet, J., Ricker, W.J.: Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions. Arch. Math. 92, 428–437 (2009)Klilou, M., Oubbi, L.: Multiplication operators on generalized weighted spaces of continuous functions. Mediterr. J. Math. 13(5), 3265–3280 (2016)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 2 (1974)Lotz, H.P.: Uniform convergence of operators on $$L^\infty$$ L ∞ and similar spaces. Math. Z. 190, 207–220 (1985)Manhas, J.S.: Compact multiplication operators on weighted spaces of vector-valued continuous functions. Rocky Mt. J. Math. 34(3), 1047–1057 (2004)Manhas, J.S.: Compact and weakly compact multiplication operators on weighted spaces of vector-valued continuous functions. Acta Sci. Math. (Szeged) 70(1–2), 361–372 (2004)Manhas, J.S., Singh, R.K.: Compact and weakly compact weighted composition operators on weighted spaces of continuous functions. Integral Equ. Oper. Theory 29(1), 63–69 (1997)Meise, R., Vogt, D.: Introduction to Functional Analysis. The Clarendon Press, Oxford University Press, New York (1997)Oubbi, L.: Multiplication operators on weighted spaces of continuous functions. Port. Math. (N.S.) 59(1), 111–124 (2002)Oubbi, L.: Weighted composition operators on non-locally convex weighted spaces. Rocky Mt. J. Math. 35(6), 2065–2087 (2005)Singh, R.K., Manhas, J.S.: Multiplication operators on weighted spaces of vector-valued continuous functions. J. Austral. Math. Soc. Ser. A 50(1), 98–107 (1991)Singh, R.K., Manhas, J.S.: Composition operators on function spaces. North-Holland Publishing Co., Amsterdam (1993)Singh, R.K., Manhas, J.S.: Operators and dynamical systems on weighted function spaces. Math. Nachr. 169, 279–285 (1994)Wilanski, A.: Topology for Analysis. Ginn, Waltham (1970)Yosida, K.: Functional Analysis. Springer, Berlin (1980

Forest carbon stocks and fluxes in physiographic zones of India

<p>Abstract</p> <p>Background</p> <p>Reducing carbon Emissions from Deforestation and Degradation (REDD+) is of central importance to combat climate change. Foremost among the challenges is quantifying nation's carbon emissions from deforestation and degradation, which requires information on forest carbon storage. Here we estimated carbon storage in India's forest biomass for the years 2003, 2005 and 2007 and the net flux caused by deforestation and degradation, between two assessment periods i.e., Assessment Period first (ASP I), 2003-2005 and Assessment Period second (ASP II), 2005-2007.</p> <p>Results</p> <p>The total estimated carbon stock in India's forest biomass varied from 3325 to 3161 Mt during the years 2003 to 2007 respectively. There was a net flux of 372 Mt of CO₂in ASP I and 288 Mt of CO₂in ASP II, with an annual emission of 186 and 114 Mt of CO₂respectively. The carbon stock in India's forest biomass decreased continuously from 2003 onwards, despite slight increase in forest cover. The rate of carbon loss from the forest biomass in ASP II has dropped by 38.27% compared to ASP I.</p> <p>Conclusion</p> <p>With the Copenhagen Accord, India along with other BASIC countries China, Brazil and South Africa is voluntarily going to cut emissions. India will voluntary reduce the emission intensity of its GDP by 20-25% by 2020 in comparison to 2005 level, activities like REDD+ can provide a relatively cost-effective way of offsetting emissions, either by increasing the removals of greenhouse gases from the atmosphere by afforestation programmes, managing forests, or by reducing emissions through deforestation and degradation.</p

Identifying divergent design thinking through the observable behavior of service design novices

© 2018, Springer Nature B.V. Design thinking holds the key to innovation processes, but is often difficult to detect because of its implicit nature. We undertook a study of novice designers engaged in team-based design exercises in order to explore the correlation between design thinking and designers’ physical (observable) behavior and to identify new, objective, design thinking identification methods. Our study addresses the topic by using data collection method of “think aloud” and data analysis method of “protocol analysis” along with the unconstrained concept generation environment. Collected data from the participants without service design experience were analyzed by open and selective coding. Through the research, we found correlations between physical activity and divergent thinking, and also identified physical behaviors that predict a designer’s transition to divergent thinking. We conclude that there are significant relations between designers’ design thinking and the behavioral features of their body and face. This approach opens possible new ways to undertake design process research and also design capability evaluation

Composition operators on function spaces

This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics. After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers