Uniqueness of unconditional bases in nonlocally convex ℓ1-products

AbstractWe show that the ℓ1-product (X⊕X⊕⋯⊕X⊕⋯)1 has a unique unconditional basis up to permutation for a wide class of nonlocally convex quasi-Banach spaces X, even without knowing whether X has a unique unconditional basis or not

On sequence spaces for Fr\'echet frames

We analyze the construction of a sequence space $\widetilde{\Theta}$, resp. a sequence of sequence spaces, in order to have $\{g_i\}$ as a $\widetilde{\Theta}$-frame or Banach frame for a Banach space $X$, resp. pre-$F$-frame or $F$-frame for a Fr\'echet space $X_F=\cap_{s\in {\mathbb N}_0} X_s$, where $\{X_s\}_{s\in {\mathbb N}_0}$ is a sequence of Banach spaces

Hydro-economic modeling with aquifer-river interactions to guide sustainable basin management

Policymakers in arid and semiarid basins face hard choices on water policies needed for adaptation to climate change. Hydro-economic modeling is a state-of-the art approach that can be used to guide the design and implementation of these policies in basins. A major gap in developments of hydro-economic modeling to date has been the weak integration of physically-based representations of water sources and uses such as the interaction between ground and surface water resources, to inform complex basin scale policy choices. This paper presents an integrated hydro-economic modeling framework to address this gap with application to an important and complex river basin in Spain, the Jucar basin, for the assessment of a range of climate change scenarios and policy choices. Results indicate that in absence of adequate policies protecting water resources and natural ecosystems, water users will strategically deplete reservoirs, aquifers and river flows for short-term adaptation to climate change, disregarding the impacts on the environment and future human activities. These impacts can be addressed by implementing sustainable management policies. However, these policies could have disproportionate costs for some stakeholders groups, and their opposition may undermine attempts at sustainable policy. These tradeoffs among water policy choices are important guides to the design of policies aimed at basin-wide adaptation to climate change

Coarse and uniform embeddings between Orlicz sequence spaces

We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper Matuszewska-Orlicz indices. On the other hand, we present examples which show that sometimes the embeddability is not determined by the values of these indices.Comment: 12 pages. This is the final version. To appear in Mediterr. J. Mat

A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page

Extendibility of bilinear forms on banach sequence spaces

[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.The second author was supported by MICINN Project MTM2011-22417.DANIEL CARANDO; Sevilla Peris, P. (2014). Extendibility of bilinear forms on banach sequence spaces. Israel Journal of Mathematics. 199(2):941-954. https://doi.org/10.1007/s11856-014-0003-9S9419541992F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Graduate Texts in Mathematics, Vol. 233, Springer, New York, 2006.R. Arens, The adjoint of a bilinear operation, Proceedings of the American Mathematical Society 2 (1951), 839–848.R. Arens, Operations induced in function classes, Monatshefte für Mathematik 55 (1951), 1–19.R. M. Aron and P. D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bulletin de la Société Mathématique de France 106 (1978), 3–24.S. Banach, Sur les fonctionelles linéaires, Studia Mathematica 1 (1929), 211–216.S. Banach, Théorie des opérations linéaires, (Monogr. Mat. 1) Warszawa: Subwncji Funduszu Narodowej. VII, 254 S., Warsaw, 1932.D. Carando, Extendible polynomials on Banach spaces, Journal of Mathematical Analysis and Applications 233 (1999), 359–372.D. Carando, Extendibility of polynomials and analytic functions on l p, Studia Mathematica 145 (2001), 63–73.D. Carando, V. Dimant and P. Sevilla-Peris, Limit orders and multilinear forms on lp spaces, Publications of the Research Institute for Mathematical Sciences 42 (2006), 507–522.J. M. F. Castillo, R. García, A. Defant, D. Pérez-García and J. Suárez, Local complementation and the extension of bilinear mappings, Mathematical Proceedings of the Cambridge Philosophical Society 152 (2012), 153–166.J. M. F. Castillo, R. García and J. A. Jaramillo, Extension of bilinear forms on Banach spaces, Proceedings of the American Mathematical Society 129 (2001), 3647–3656.P. Cembranos and J. Mendoza, The Banach spaces ℓ ∞(c 0) and c 0(ℓ ∞) are not isomorphic, Journal of Mathematical Analysis and Applications 367 (2010), 461–463.A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, Vol. 176, North-Holland Publishing Co., Amsterdam, 1993.A. Defant and C. Michels, Norms of tensor product identities, Note di Matematica 25 (2005/06), 129–166.J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, Vol. 43, Cambridge University Press, Cambridge, 1995.D. J. H. Garling, On symmetric sequence spaces, Proceedings of the London Mathematical Society (3) 16 (1966), 85–106.A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1–79.H. Hahn, Über lineare Gleichungssysteme in linearen Räumen, Journal für die Reine und Angewandte Mathematik 157 (1927), 214–229.R. C. James, Bases and reflexivity of Banach spaces, Annals of Mathematics (2) 52 (1950), 518–527.H. Jarchow, C. Palazuelos, D. Pérez-García and I. Villanueva, Hahn-Banach extension of multilinear forms and summability, Journal of Mathematical Analysis and Applications 336 (2007), 1161–1177.W. B. Johnson and L. Tzafriri, On the local structure of subspaces of Banach lattices, Israel Journal of Mathematics 20 (1975), 292–299.P. Kirwan and R. A. Ryan, Extendibility of homogeneous polynomials on Banach spaces, Proceedings of the American Mathematical Society 126 (1998), 1023–1029.J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in Lp-spaces and their applications, Studia Mathematica 29 (1968), 275–326.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], Vol. 97, Springer-Verlag, Berlin, 1979. Function spaces.G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conference Series in Mathematics, Vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1986.M. Fernndez-Unzueta and A. Prieto, Extension of polynomials defined on subspaces, Mathematical Proceedings of the Cambridge Philosophical Society 148 (2010), 505–518.W. L. C. Sargent, Some sequence spaces related to the lp spaces, Journal of the London Mathematical Society 35 (1960), 161–171.N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 38, Longman Scientific & Technical, Harlow, 1989