scholarly journals A few remarks on bounded operators on topological vector spaces

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 763-772
Author(s):  
Omid Zabeti ◽  
Ljubisa Kocinac
Keyword(s):  
Tensor Product ◽  
Vector Space ◽  
Topological Vector Space ◽  
Compact Operators ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Bounded Operators ◽  
Topological Vector Spaces ◽  
Different Types ◽  
Locally Convex

We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators. We also consider similar types of bounded bilinear mappings between topological vector spaces. Some properties of tensor product operators between locally convex spaces are established. In the last part of the paper we deal with operators on topological Riesz spaces.

On the Nonstandard Duality Theory of Locally Convex Spaces

1980 ◽  
Vol 32 (2) ◽  
pp. 460-479 ◽  
Author(s):  
Arthur D. Grainger
Keyword(s):  
Vector Space ◽  
Duality Theory ◽  
Dual System ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Nonstandard Model ◽  
Locally Convex ◽  
External Property ◽  
Convex Spaces

This paper continues the nonstandard duality theory of locally convex, topological vector spaces begun in Section 5 of [3]. In Section 1, we isolate an external property, called the pseudo monad, that appears to be one of the central concepts of the theory (Definition 1.2). In Section 2, we relate the pseudo monad to the Fin operation. For example, it is shown that the pseudo monad of a µ-saturated subset A of *E, the nonstandard model of the vector space E, is the smallest subset of A that generates Fin (A) (Proposition 2.7).The nonstandard model of a dual system of vector spaces is considered in Section 3. In this section, we use pseudo monads to establish relationships among infinitesimal polars, finite polars (see (3.1) and (3.2)) and the Fin operation (Theorem 3.7).

scholarly journals Bounded operators on topological vector spaces and their spectral radii

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1283-1290
Author(s):  
Shirin Hejazian ◽  
Madjid Mirzavaziri ◽  
Omid Zabeti
Keyword(s):  
Linear Operator ◽  
Vector Space ◽  
Topological Vector Space ◽  
Bounded Linear Operator ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Vector Spaces ◽  
Bounded Operators ◽  
Bounded Linear ◽  
Topological Vector Spaces

In this paper, we consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some properties for the spectral radii of a linear operator on a topological vector space. We find some sufficient conditions for the completeness of these classes of operators. Finally, as a special application, we deduce some sufficient conditions for invertibility of a bounded linear operator.

scholarly journals Some properties of vector measures taking values in a topological vector space

1987 ◽  
Vol 43 (2) ◽  
pp. 224-230
Author(s):  
Efstathios Giannakoulias
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Vector Spaces ◽  
Necessary Condition ◽  
Vector Measures ◽  
Topological Vector Spaces ◽  
Locally Convex ◽  
Pettis Integrability

AbstractIn this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function f: S → E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.

scholarly journals ωb-Topological Vector Spaces

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Vector Spaces ◽  
Closed Set ◽  
Topological Vector Spaces ◽  
New Class ◽  
Fundamental Properties ◽  
General Properties

The purpose of the present paper is to introduce the new class of ω b - topological vector spaces. We study several basic and fundamental properties of ω b - topological and investigate their relationships with certain existing spaces. Along with other results, we prove that transformation of an open (resp. closed) set in aω b - topological vector space is ω b - open (resp. closed). In addition, some important and useful characterizations of ω b - topological vector spaces are established. We also introduce the notion of almost ω b - topological vector spaces and present several general properties of almost ω b - topological vector spaces.

scholarly journals M – STAR – Irresolute Topological Vector Spaces

2021 ◽  
Vol 7 ◽  
pp. 20-36
Author(s):  
Raja Mohammad Latif
Keyword(s):  
Vector Space ◽  
Extreme Point ◽  
Topological Vector Space ◽  
Convex Subset ◽  
Hausdorff Space ◽  
Vector Spaces ◽  
Topological Spaces ◽  
Topological Vector Spaces ◽  
New Class

In 2016 A. Devika and A. Thilagavathi introduced a new class of sets called M*-open sets and investigated some properties of these sets in topological spaces. In this paper, we introduce and study a new class of spaces, namely M*-irresolute topological vector spaces via M*-open sets. We explore and investigate several properties and characterizations of this new notion of M*-irresolute topological vector space. We give several characterizations of M*-Hausdorff space. Moreover, we show that the extreme point of the convex subset of M*-irresolute topological vector space X lies on the boundary.

An Embedding Theorem for Separable Locally Convex Spaces

1971 ◽  
Vol 14 (1) ◽  
pp. 119-120 ◽  
Author(s):  
Robert H. Lohman
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Space ◽  
Separable Banach Space ◽  
Locally Convex Space ◽  
Embedding Theorem ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Locally Convex

A well-known embedding theorem of Banach and Mazur [1, p. 185] states that every separable Banach space is isometrically isomorphic to a subspace of C[0, 1], establishing C[0, 1] as a universal separable Banach space. The embedding theorem one encounters in a course in topological vector spaces states that every Hausdorff locally convex space (l.c.s.) is topologically isomorphic to a subspace of a product of Banach spaces.

On C-sequences of operators

2003 ◽  
Vol 40 (1-2) ◽  
pp. 145-150
Author(s):  
B. Wang
Keyword(s):  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Operator Series ◽  
Locally Convex ◽  
Convex Spaces

Invariant results are established for a considerably general multiplier convergence of operator series where the operators are defined on arbitrary topological vector spaces and valued in arbitrary locally convex spaces.

XI.—On Unconditional Convergence in Topological Vector Spaces

1969 ◽  
Vol 68 (2) ◽  
pp. 145-157 ◽  
Author(s):  
A. P. Robertson
Keyword(s):  
Sufficient Conditions ◽  
Direct Proof ◽  
Vector Spaces ◽  
Unconditional Convergence ◽  
Partial Sums ◽  
Locally Convex Spaces ◽  
Topological Groups ◽  
Topological Vector Spaces ◽  
Necessary And Sufficient ◽  
Locally Convex

SynopsisFor a series of elements of a topological vector space, necessary and sufficient conditions are found, in terms of the set of finite partial sums, for unconditional convergence and for the corresponding Cauchy condition. The extent to which these results remain valid for topological groups is investigated. A new and direct proof, for locally convex spaces, is given of the theorem of Orlicz.

scholarly journals Characterizations of collectively precompact and semi-precompact opterators on topological vector spaces

1979 ◽  
Vol 28 (2) ◽  
pp. 179-188 ◽  
Author(s):  
M. V. Deshpande ◽  
S. M. Padhye
Keyword(s):  
Subject Classification ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Totally Bounded ◽  
Primary 47 ◽  
Bounded Sets ◽  
Locally Convex ◽  
Convex Spaces

AbstractCharacterizations of collectively precompact and collectively semi-precompact sets of operators on topological vector spaces are obtained. These lead to the characterization of totally bounded sets of semi-precompact operators on locally convex spaces.1980 Mathematics subject classification (Amer. Math. Soc): primary 47 B 05, 47 D 15; secondary 46 A 05, 46 A 15.

scholarly journals Webbed spaces, double sequences, and the Macke convergence condition

1999 ◽  
Vol 22 (3) ◽  
pp. 521-524
Author(s):  
Armando García-Martínez
Keyword(s):  
Convergence Condition ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Double Sequences ◽  
Localization Theorem ◽  
Topological Vector Spaces ◽  
General Frame ◽  
Locally Convex ◽  
Webbed Space ◽  
Convex Spaces

In [3], Gilsdorf proved, for locally convex spaces, that every sequentially webbed space satisfies the Mackey convergence condition. In the more general frame of topological vector spaces, this theorem and its inverse are studied. The techniques used are double sequences and the localization theorem for webbed spaces.

Sign in / Sign up

Export Citation Format

Share Document