Related papers: Similarities and differences between real and comp…

In this paper, we define probabilistic n-Banach spaces along with some concepts in this field and study convergence in these spaces by some lemmas and theorem.

This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…

This paper is essentially a survey on several classical results of harmonic analysis and their recent extensions to Banach spaces. The first part of the paper is a summary of some important results in such topics as Bernstein spaces,…

A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…

It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is…

In this article, concepts of well- and ill-posedness for linear operators in Hilbert and Banach spaces are discussed. While these concepts are well understood in Hilbert spaces, this is not the case in Banach spaces, as there are several…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.

This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…

All most all the function spaces over real or complex domains and spaces of sequences, that arise in practice as examples of normed complete linear spaces (Banach spaces), are reflexive. These Banach spaces are dual to their respective…

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$.…

In a recent paper by the authors a general result characterizing two-sided LIL behavior for real valued random variables has been established. In this paper, we show that there are analogous results in the Banach space setting. One of our…

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable…

In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space…

We study Birkhoff-James orthogonality of bounded linear operators on complex Banach spaces and obtain a complete characterization of the same. By means of introducing new definitions, we illustrate that it is possible in the complex case,…

In this note, we introduce and study the left (right) pseudospectrum and left (right) condition pseudospectrum of bounded linear operators on ultrametric Banach spaces. We prove some results about them.

We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are…

We prove several dichotomies on linear embeddings between Banach spaces. Given an arbitrary Banach space X with a basis, we show that the relations of isomorphism and bi-embedding are meager or co-meager on the Polish set of block-subspaces…

In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…

These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the…

In this survey, we consider Banach spaces of analytic functions in one and several complex variables for which: (i) polynomials are dense, (ii) point-evaluations on the domain are bounded linear functionals, and (iii) the shift operator…