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 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.

scholarly journals Class of bounded operators associated with an atomic system

2014 ◽  
Vol 46 (1) ◽  
pp. 85-90 ◽  
Author(s):  
P.Sam Johnson ◽  
G. Ramu
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Atomic System ◽  
Linear Operators ◽  
Bounded Operators ◽  
Frame Operator ◽  
Bessel Sequence ◽  
Bounded Linear ◽  
Atomic Systems

$K$-frames, more general than the ordinary frames, have been introduced by Laura G{\u{a}}vru{\c{t}}a in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Using the frame operator, we find a class of bounded linear operators in which a given Bessel sequence is an atomic system for every member in the class.

scholarly journals BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY

2007 ◽  
Vol 49 (1) ◽  
pp. 145-154
Author(s):  
BRUCE A. BARNES
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Integral Operators ◽  
Continuous Functions ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Spaces Of Continuous Functions

Abstract.LetTbe a bounded linear operator on a Banach spaceW, assumeWandYare in normed duality, and assume thatThas adjointT†relative toY. In this paper, conditions are given that imply that for all λ≠0, λ−Tand λ −T†maintain important standard operator relationships. For example, under the conditions given, λ −Thas closed range if, and only if, λ −T†has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

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.

A Note on the Caradus Class of Bounded Linear Operators on a Complex Banach Space

1969 ◽  
Vol 21 ◽  
pp. 592-594 ◽  
Author(s):  
A. F. Ruston
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Finite Number ◽  
Bounded Linear Operator ◽  
Present Note ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Subject

1. In a recent paper (1) on meromorphic operators, Caradus introduced the class of bounded linear operators on a complex Banach space X. A bounded linear operator T is put in the class if and only if its spectrum consists of a finite number of poles of the resolvent of T. Equivalently, T is in if and only if it has a rational resolvent (8, p. 314).Some ten years ago (in May, 1957), I discovered a property of the class g which may be of interest in connection with Caradus' work, and is the subject of the present note.2. THEOREM. Let X be a complex Banach space. If T belongs to the class, and the linear operator S commutes with every bounded linear operator which commutes with T, then there is a polynomial p such that S = p(T).

(F,G)-operator frames for ℒ(ℋ,𝒦)

2020 ◽  
Vol 18 (05) ◽  
pp. 2050031
Author(s):  
J. Sedghi Moghaddam ◽  
A. Najati ◽  
F. Ghobadzadeh
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Bounded Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Atomic Systems ◽  
Pseudo Inverse

The concept of [Formula: see text]-frames was recently introduced by Găvruta7 in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Let [Formula: see text] be a unital [Formula: see text]-algebra, [Formula: see text] be finitely or countably generated Hilbert [Formula: see text]-modules, and [Formula: see text] be adjointable operators from [Formula: see text] to [Formula: see text]. In this paper, we study a class of [Formula: see text]-bounded operators and [Formula: see text]-operator frames for [Formula: see text]. We also prove that the pseudo-inverse of [Formula: see text] exists if and only if [Formula: see text] has closed range. We extend some known results about the pseudo-inverses acting on Hilbert spaces in the context of Hilbert [Formula: see text]-modules. Further, we also present some perturbation results for [Formula: see text]-operator frames in [Formula: see text].

scholarly journals On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Karim Hedayatian ◽  
Lotfollah Karimi
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Bounded Linear Operator ◽  
Sufficient Conditions ◽  
Multiplication Operators ◽  
Weighted Hardy Spaces ◽  
Bounded Linear ◽  
Necessary And Sufficient

A bounded linear operatorTon a Hilbert spaceℋ, satisfying‖T2h‖2+‖h‖2≥2‖Th‖2for everyh∈ℋ, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convex composition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators.

scholarly journals Some special characterisations of Fredholm operators in Banach space

BIBECHANA ◽  
2014 ◽  
Vol 11 ◽  
pp. 169-174
Author(s):  
Mahendra Shahi
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Essential Spectrum ◽  
Fredholm Operator ◽  
Bounded Linear Operator ◽  
Global Analysis ◽  
Spectral Theorem ◽  
Bounded Operators ◽  
Fredholm Operators ◽  
Bounded Linear

A bounded linear operator which has a finite index and which is defined on a Banach space is often referred to in the literature as a Fredholm operator. Fredholm operators are important for a variety of reasons, one being the role that their index plays in global analysis. The aim of this paper is to prove the spectral theorem for compact operators in refined form and to describe some properties of the essential spectrum of general bounded operators by the use of the theorem of Fredholm operators. For this, we have analysed the Fredholm operator which is defined in a Banach space for some special characterisations. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10399 BIBECHANA 11(1) (2014) 169-174

Representation of certain Linear Operators in Hilbert Space

1971 ◽  
Vol 23 (1) ◽  
pp. 132-150 ◽  
Author(s):  
Bernard Niel Harvey
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Separable Hilbert Space ◽  
Finite Dimension ◽  
Linear Operators ◽  
Inner Product ◽  
Indefinite Metric ◽  
Bounded Linear ◽  
Bilinear Functional

In this paper we represent certain linear operators in a space with indefinite metric. Such a space may be a pair (H, B), where H is a separable Hilbert space, B is a bilinear functional on H given by B(x, y) = [Jx, y], [, ] is the Hilbert inner product in H, and J is a bounded linear operator such that J = J* and J2 = I. If T is a linear operator in H, then ‖T‖ is the usual operator norm. The operator J above has two eigenspaces corresponding to the eigenvalues + 1 and –1.In case the eigenspace in which J induces a positive operator has finite dimension k, a general spectral theory is known and has been developed principally by Pontrjagin [25], Iohvidov and Kreĭn [13], Naĭmark [20], and others.

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