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Displaying 681 – 700 of 3161

Corrigendum to the paper “The universal Banach space with a $K$ -suppression unconditional basis”

Taras O. Banakh, Joanna Garbulińska-Wegrzyn (2020)

Commentationes Mathematicae Universitatis Carolinae

We observe that the notion of an almost ${𝔉ℑ}_{K}$ -universal based Banach space, introduced in our earlier paper [1]: Banakh T., Garbulińska-Wegrzyn J., The universal Banach space with a $K$ -suppression unconditional basis, Comment. Math. Univ. Carolin. 59 (2018), no. 2, 195–206, is vacuous for $K = 1$ . Taking into account this discovery, we reformulate Theorem 5.2 from [1] in order to guarantee that the main results of [1] remain valid.

Cotype and absolutely summing homogeneous polynomials in $ℒ_{p}$ spaces

Daniel Pellegrino (2003)

Studia Mathematica

We lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pełczyński for absolutely summing operators. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which the space of absolutely summing homogeneous polynomials is different from the whole space of homogeneous polynomials. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing homogeneous...

Cotype and complemented copies of $c_{0}$ in spaces of operators

J. Bonet, Paweł Domański, M. Lindström (1996)

Czechoslovak Mathematical Journal

Cotype and (q, 1)-summing norm in a Banach space.

Michel Talagrand (1992)

Inventiones mathematicae

Cotype for p-Banach spaces

Jesús Bastero, Zenaida Uriz (1986)

Compositio Mathematica

Cotype of operators from C(K).

Michel Talagrand (1992)

Inventiones mathematicae

Countable products of spaces of finite sets

Antonio Avilés (2005)

Fundamenta Mathematicae

We consider the compact spaces σₙ(Γ) of subsets of Γ of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.

Countably convex $G_{δ}$ sets

Vladimir Fonf, Menachem Kojman (2001)

Fundamenta Mathematicae

We investigate countably convex $G_{δ}$ subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets this condition...

Criteria for $k_{M} < \infty$ in Musielak-Orlicz spaces

Lianying Cao, Ting Fu Wang (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper, some necessary and sufficient conditions for $sup {k_{x} : ∥ x ∥^{0} = 1} < \infty$ in Musielak-Orlicz function spaces as well as in Musielak-Orlicz sequence spaces are given.

Darstellung von Banach-Verbänden und Sätze vom Korovkin-Typ.

Manfred Wolff (1973)

Mathematische Annalen

Das Spektrum von Verbandsoperatoren in Banachverbänden.

Egon Scheffold (1971)

Mathematische Zeitschrift

Daugavet centers and direct sums of Banach spaces

Tetiana Bosenko (2010)

Open Mathematics

A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center...

De la recherche pétrolière à la géométrie des espaces de Banach en passant par les paraproduits

Y. Meyer (1985/1986)

Séminaire Équations aux dérivées partielles (Polytechnique)

De nouveaux espaces de Banach sans la propriété d'approximation

Gilles Pisier (1978/1979)

Séminaire Bourbaki

Decomposable subspaces of Banach spaces.

Manuel González, Antonio Martinón (2003)

RACSAM

We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ+(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

Plichko, Anatolij (1997)

Serdica Mathematical Journal

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis. If a Banach space E cannot...

Decompositions for real Banach spaces with small spaces of operators

Manuel González, José M. Herrera (2007)

Studia Mathematica

We consider real Banach spaces X for which the quotient algebra (X)/ℐn(X) is finite-dimensional, where ℐn(X) stands for the ideal of inessential operators on X. We show that these spaces admit a decomposition as a finite direct sum of indecomposable subspaces $X_{i}$ for which $(X_{i}) / ℐ n (X_{i})$ is isomorphic as a real algebra to either the real numbers ℝ, the complex numbers ℂ, or the quaternion numbers ℍ. Moreover, the set of subspaces $X_{i}$ can be divided into subsets in such a way that if $X_{i}$ and $X_{j}$ are in different subsets,...

Deformation of Banach spaces

Józef Banaś, Krzysztof Fraczek (1993)

Commentationes Mathematicae Universitatis Carolinae

Using some moduli of convexity and smoothness we introduce a function which allows us to measure the deformation of Banach spaces. A few properties of this function are derived and its applicability in the geometric theory of Banach spaces is indicated.

Degree of convexity and product spaces

Emanuele Casini (1990)

Commentationes Mathematicae Universitatis Carolinae

Demand continuity and equilibrium in Banach commodity spaces

Anthony Horsley, A. J. Wrobel (2006)

Banach Center Publications

Norm-to-weak* continuity of excess demand as a function of prices is proved by using our two-topology variant of Berge's Maximum Theorem. This improves significantly upon an earlier result that, with the extremely strong finite topology on the price space, is of limited interest, except as a vehicle for proving equilibrium existence. With the norm topology on the price space, our demand continuity result becomes useful in applications of equilibrium theory, especially to problems with continuous...

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