Notation. ε is an arbitrarily small positive number. L(X,Y ) is the Banach space of bounded linear operators T : X → Y . B(X) is the closed unit ball {x ∈ X : ‖x‖ 6 1}. N := N ∪ {∞} is the one-point compactification of the discrete space N. All operators are bounded and linear. A compact (topological) space always means a compact Hausdorff space. (We sometimes add “Hausdorff” explicitly for emp...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

We show that every complete metric space is homeomorphic to the locus of zeros of an entire analytic map from a complex Hilbert space to a complex Banach space. As a corollary, every separable complete metric space is homeomorphic to the locus of zeros of an entire analytic map between two complex Hilbert spaces. §1. Douady had observed [8] that every compact metric space is homeomorphic to the...

Let X be a Banach space and (Ω,Σ) be a measure space. We provide a characterization of sequences in the space of X-valued countably additive measures on (Ω,Σ) of bounded variation that generates complemented copies of l1. As application, we prove that if a dual Banach space E∗ has Pe lczyński’s property (V*) then so does the space of E∗-valued countably additive measures with the variation norm...

The present thesis deals with computable functional analysis and in this context, especially, with compact operators on computable Banach spaces. For this purpose, the representation based approach to computable analysis (TTE) is used. In the first part, computable Banach spaces with computable Schauder bases are introduced and two representations each are defined for the dual space of a comput...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

We extend the Paley-Wiener pertubation theory to linear operators mapping a subspace of one Banach space into another Banach space.

We extend the Paley-Wiener pertubation theory to linear operators mapping a subspace of one Banach space into another Banach space.

A fundamental question in operator theory is: how rich is the collection of oprrators on a given Banach space? For classical spaces, especially Hilbert space, a well developed theory of operators exists. However a Banach space may have far fewer operators than one might expect. Shelah [S] has constructed a nonseparable Ba~lach space X , for which the space of operators with separable range has ...

Unless we say otherwise, every vector space we talk about is taken to be over C. A Banach algebra is a Banach space A that is also an algebra satisfying ‖AB‖ ≤ ‖A‖ ‖B‖ for A,B ∈ A. We say that A is unital if there is a nonzero element I ∈ A such that AI = A and IA = A for all A ∈ A, called a identity element. If X is a Banach space, let B(X) denote the set of bounded linear operators X → X, and...