An approach to generalizing Banach spaces: normed almost linear spaces
An approximation property with respect to an operator ideal
Given an operator ideal , we say that a Banach space X has the approximation property with respect to if T belongs to for every Banach space Y and every T ∈ (Y,X), being the topology of uniform convergence on compact sets. We present several characterizations of this type of approximation property. It is shown that some of the existing approximation properties in the literature may be included in this setting.
An Arithmetic Characterization of Decomposition Methods in Banach Spaces Similar to Pełczyński's Decomposition Method
Inspired by Pełczyński's decomposition method in Banach spaces, we introduce the notion of Schroeder-Bernstein quadruples for Banach spaces. Then we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.
An elementary approach to some questions in higher order smoothness in Banach spaces.
An Elementary Characterization of Absolutely Summing Operators.
An embedding of the algebra of order bounded operators on a Dedekind complete Banach lattice.
An essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish patriot
An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and
An exact Ramsey principle for block sequences.
An Example Concerning Valdivia Compact Spaces
∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998We prove that the dual unit ball of the space C0 [0, ω1 ) endowed with the weak* topology is not a Valdivia compact. This answers a question posed to the author by V. Zizler and has several consequences. Namely, it yields an example of an affine continuous image of a convex Valdivia compact (in the weak* topology of a dual Banach space) which is not Valdivia, and shows that the property of the dual unit ball being Valdivia is not an isomorphic...
An example of a function, which is not a d.c. function
Let , . We construct a function which has Lipschitz Fréchet derivative on but is not a d.c. function.
An example of a normal space non-isomorphic to its product by the real line
An example of infinite dimensional reflexive Banach space non-isomorphic to its Cartesian square
An example of infinite dimensional reflexive space non-isomorphic to its cartesian square
An exponential law for regular ordered Banach spaces
An extension of Helly's theorem for Banach spaces
An extension of Lorentz's almost convergence and applications in Banach spaces
2000 Mathematics Subject Classification: Primary 40C99, 46B99.We investigate an extension of the almost convergence of G. G. Lorentz requiring that the means of a bounded sequence converge uniformly on a subset M of N. We also present examples of sequences α∈ l∞(N) whose sequences of translates (Tn α)n≥ 0 (where T is the left-shift operator on l∞(N)) satisfy: (a) Tn α, n ≥ 0 generates a subspace E(α) of l∞(N) that is isomorphically embedded into c0 while α is not almost convergent. (b) Tn...
An Extension of Milman's Reverse Brunn-Minkowski Inequality.
An extension of Simons' inequality and applications.
This article is devoted to an extension of Simons' inequality. As a consequence, having a pointwise converging sequence of functions, we get criteria of uniform convergence of an associated sequence of functions.
An extension of the Krein-Smulian theorem.
Let X be a Banach space, u ∈ X** and K, Z two subsets of X**. Denote by d(u,Z) and d(K,Z) the distances to Z from the point u and from the subset K respectively. The Krein-Smulian Theorem asserts that the closed convex hull of a weakly compact subset of a Banach space is weakly compact; in other words, every w*-compact subset K ⊂ X** such that d(K,X) = 0 satisfies d(cow*(K),X) = 0.We extend this result in the following way: if Z ⊂ X is a closed subspace of X and K ⊂ X** is a w*-compact subset of...