Results 21 to 30 of about 507 (79)

Bornological convergences and local proximity spaces

Topology and its Applications, 2014
Local proximity spaces were introduced by \textit{S. Leader} in [Math. Ann. 169, 275--281 (1967; Zbl 0144.21702)]; they consist of a set, \(X\), a proximity, \(\delta\), on~\(X\), and a family of subsets, \(\mathcal{B}\), that are deemed to be `bounded'. Their interrelation is such that it mimics the behaviour of the family of compact sets in a locally
DI CONCILIO, Anna, GUADAGNI, CLARA
openaire   +4 more sources

Operator Ideals arising from Generating Sequences [PDF]

, 2011
In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be ...
Wong, Ngai-Ching
core   +1 more source

Buchwalter‐Schmets theorems and linear topologies

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 13-16, 1999., 1999
In this paper, we obtain Buchwalter‐Schmets theorems in the realm of Lefschetz linearly topologized spaces.
L. M. Sánchez Ruiz, J. R. Ferrer
wiley   +1 more source

Relations between exponential laws for spaces of C∞‐functions

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 209-218, 1997., 1995
In this paper we prove that some new as well as some already existing exponential laws for spaces of C∞‐ and holomorphic functions can all be generated from one general exponential law.
Peter Biström
wiley   +1 more source

Set Convergences via Bornology

Set-Valued and Variational Analysis
This paper examines the equivalence between various set convergences, as studied in [7, 13, 22], induced by an arbitrary bornology $\mathcal{S}$ on a metric space $(X,d)$. Specifically, it focuses on the upper parts of the following set convergences: convergence deduced through uniform convergence of distance functionals on $\mathcal{S}$ ($τ_{\mathcal ...
Agarwal, Yogesh, Jindal, Varun
openaire   +3 more sources

Closed graph theorems for bornological spaces

, 2015
The aim of this paper is that of discussing Closed Graph Theorems for bornological vector spaces in a way which is accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over $\mathbb{R}$ and $\mathbb{C}$ to
Bambozzi, Federico
core   +1 more source

Arzelà's Theorem and strong uniform convergence on bornologies

Journal of Mathematical Analysis and Applications, 2010
The main result of this nice paper (Theorem 2.9) gives a direct proof that three kinds of convergence (Arzelà's convergence on compacta, Alexandroff's convergence and strong uniform convergence on finite sets, introduced recently by \textit{G. Beer} and \textit{S. Levi} [J. Math. Anal. Appl.
Caserta, Agata, Di Maio, Giuseppe, Holá, L˘ubica   +2 more
openaire   +3 more sources

Functional analysis on two-dimensional local fields

, 2013
We establish how a two-dimensional local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we study bounded, c-
Camara, Alberto
core   +1 more source

Mackey convergence and quasi‐sequentially webbed spaces

International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 1, Page 17-26, 1991., 1991
The problem of characterizing those locally convex spaces satisfying the Mackey convergence condition is still open. Recently in [4], a partial description was given using compatible webs. In this paper, those results are extended by using quasi‐sequentially webbed spaces (see Definition 1).
Thomas E. Gilsdorf
wiley   +1 more source

On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution [PDF]

, 2017
We develop a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and use it as a base for the parametrix method in the study of new topological and structural properties ...
Pilipovic, Stevan, Prangoski, Bojan, Vindas, Jasson   +2 more
core   +2 more sources