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...

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an M-ideal in the space of bounded operators, a very smooth operator T attains its norm at a unique vector x (up to a constant multiple) and T (x) is a very smooth point of the range space. We show that if for every equivalent norm on a Ban...

The Laplace transform theory of Banach space valued functions and the field of evolution equations presently offer many research problems which are of general interest in mathematical analysis. Although there is a longstanding relationship between the two fields, it was not until recently that the basic transform principles for Banach space valued functions could be formulated in a satisfactory...

We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of ...