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Constructing non-compact operators into c₀

Iryna Banakh; Taras Banakh — 2010

Studia Mathematica

We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.

Extenders for vector-valued functions

Iryna Banakh; Taras Banakh; Kaori Yamazaki — 2009

Studia Mathematica

Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender $u : C_{\infty} (A, Y) \to C_{\infty} (X, Y)$ , which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained allow us...

Topological Structure of Non-separable Sigma-locally Compact Convex Sets

Iryna Banakh; Taras Banakh; Katsuhisa Koshino — 2013

Bulletin of the Polish Academy of Sciences. Mathematics

On local convexity of nonlinear mappings between Banach spaces

Iryna Banakh; Taras Banakh; Anatolij Plichko; Anatoliy Prykarpatsky — 2012

Open Mathematics

We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.

On $r$ -reflexive Banach spaces

Iryna Banakh; Taras O. Banakh; Elena Riss — 2009

Commentationes Mathematicae Universitatis Carolinae

A Banach space $X$ is called if for any cover $𝒰$ of $X$ by weakly open sets there is a finite subfamily $𝒱 \subset 𝒰$ covering some ball of radius 1 centered at a point $x$ with $∥ x ∥ \leq r$ . We prove that an infinite-dimensional separable Banach space $X$ is $\infty$ -reflexive ( $r$ -reflexive for some $r \in ℕ$ ) if and only if each $ε$ -net for $X$ has an accumulation point (resp., contains a non-trivial convergent sequence) in the weak topology of $X$ . We show that the quasireflexive James space $J$ is $r$ -reflexive for no $r \in ℕ$ . We do not know if each $\infty$ -reflexive...

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Currently displaying 1 – 5 of 5

Constructing non-compact operators into c₀

Extenders for vector-valued functions

Topological Structure of Non-separable Sigma-locally Compact Convex Sets

On local convexity of nonlinear mappings between Banach spaces

On $r$ -reflexive Banach spaces

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Constructing non-compact operators into c₀

Extenders for vector-valued functions

Topological Structure of Non-separable Sigma-locally Compact Convex Sets

On local convexity of nonlinear mappings between Banach spaces

On r -reflexive Banach spaces

On $r$ -reflexive Banach spaces