scholarly journals On the extension of linear operators

2001 ◽  
Vol 28 (10) ◽  
pp. 621-623 ◽  
Author(s):  
John J. Saccoman
Keyword(s):  
Extension Theorem ◽  
Linear Operators ◽  
Two Dimensional ◽  
Linear Functionals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Banach Theorem

It is well known that the Hahn-Banach theorem, that is, the extension theorem for bounded linear functionals, is not true in general for bounded linear operators. A characterization of spaces for which it is true was published by Kakutani in 1940. We summarize Kakutani's work and we give an example which demonstrates that his characterization is not valid for two-dimensional spaces.

Generators of Nest Algebras

1974 ◽  
Vol 26 (3) ◽  
pp. 565-575 ◽  
Author(s):  
W. E. Longstaff
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Nest Algebra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Algebra ◽  
Nest Algebras ◽  
Weakly Closed

A collection of subspaces of a Hilbert space is called a nest if it is totally ordered by inclusion. The set of all bounded linear operators leaving invariant each member of a given nest forms a weakly-closed algebra, called a nest algebra. Nest algebras were introduced by J. R. Ringrose in [9]. The present paper is concerned with generating nest algebras as weakly-closed algebras, and in particular with the following question which was first raised by H. Radjavi and P. Rosenthal in [8], viz: Is every nest algebra on a separable Hilbert space generated, as a weakly-closed algebra, by two operators? That the answer to this question is affirmative is proved by first reducing the problem using the main result of [8] and then by using a characterization of nests due to J. A. Erdos [2].

Stability of the S-essential spectra on a Banach space

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Faiçal Abdmouleh ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Essential Spectra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Projection

AbstractIn this paper, we give the characterization of S-essential spectra, we define the S-Riesz projection and we investigate the S-Browder resolvent. Finally, we study the S-essential spectra of sum of two bounded linear operators acting on a Banach space.

scholarly journals An algebraic characterization of complete inner product spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 47-53
Author(s):  
Vasile I. Istratescu
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Inner Product ◽  
Algebraic Characterization ◽  
Product Spaces ◽  
Bounded Linear Operators ◽  
Multiplicative Property ◽  
Bounded Linear ◽  
Inner Product Spaces

We present a characterization of complete inner product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a “multiplicative” property of the norm for hermitain operators. In the second part we present a simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj.

Characterization of linear preservers of generalized majorization on c0

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4979-4988 ◽  
Author(s):  
Eshkaftaki Bayati ◽  
Noha Eftekhari
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Supremum Norm ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Linear Preservers

In this work we investigate a natural preorder on c0, the Banach space of all real sequences tend to zero with the supremum norm, which is said to be ?convex majorization?. Some interesting properties of all bounded linear operators T : c0 ? c0, preserving the convex majorization, are given and we characterize such operators.

Characterization of two-sided order preserving of convex majorization on lp(I)

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5703-5710 ◽  
Author(s):  
Ali Eshkaftaki ◽  
Noha Eftekhari
Keyword(s):  
Equivalence Relation ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

In this paper, we consider an equivalence relation ~c on lp(I), which is said to be ?convex equivalent? for p ? [1,+?) and a nonempty set I. We characterize the structure of all bounded linear operators T : lp(I) ? lp(I) that strongly preserve the convex equivalence relation. We prove that the rows of the operator which preserve convex equivalent, belong to l1(I): Also, we show that any bounded linear operators T : lp(I) ? lp(I) which preserve convex equivalent, also preserve convex majorization.

scholarly journals Spectrality of elementary operators

1990 ◽  
Vol 49 (2) ◽  
pp. 327-346 ◽  
Author(s):  
Milan Hladnik
Keyword(s):  
Complete Characterization ◽  
Linear Operators ◽  
Schatten Classes ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Normal Operators ◽  
Elementary Operators

AbstractSpectrality and prespectrality of elementary operators , acting on the algebra B(k) of all bounded linear operators on a separable infinite-dimensional complex Hubert space K, or on von Neumann-Schatten classes in B(k), are treated. In the case when (a1, a2, …, an) and (b1, b2, …, bn) are two n—tuples of commuting normal operators on H, the complete characterization of spectrality is given.

scholarly journals ORTHOGONALITY AND PARALLELISM OF OPERATORS ON VARIOUS BANACH SPACES

2018 ◽  
Vol 106 (2) ◽  
pp. 160-183 ◽  
Author(s):  
T. BOTTAZZI ◽  
C. CONDE ◽  
M. S. MOSLEHIAN ◽  
P. WÓJCIK ◽  
A. ZAMANI
Keyword(s):  
Banach Spaces ◽  
Compact Operators ◽  
Linear Operators ◽  
Identity Operator ◽  
Uniformly Convex ◽  
Bounded Linear Operators ◽  
Norm Inequalities ◽  
Bounded Linear ◽  
Uniformly Convex Spaces

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in $p$-Schatten ideals. In addition, we investigate the problem of characterization of norm-parallelism for bounded linear operators. We consider the characterization of the norm-parallelism problem in $p$-Schatten ideals and locally uniformly convex spaces. Later on, we study the case when an operator is norm-parallel to the identity operator. Finally, we give some equivalence assertions about the norm-parallelism of compact operators. Some applications and generalizations are discussed for certain operators.

scholarly journals A complete characterization of smoothness in the space of bounded linear operators

2019 ◽  
Vol 68 (12) ◽  
pp. 2484-2494 ◽  
Author(s):  
Debmalya Sain ◽  
Kallol Paul ◽  
Arpita Mal ◽  
Anubhab Ray
Keyword(s):  
Complete Characterization ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

scholarly journals A characterization of real and complex Hilbert spaces among all normed spaces

1983 ◽  
Vol 27 (3) ◽  
pp. 339-345
Author(s):  
J. Vukman
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Linear Operators ◽  
Identity Operator ◽  
Normed Spaces ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Finite Dimensional ◽  
Dimensional Range

Let X be a real or complex normed space and L(X) the algebra of all bounded linear operators on X. Suppose there exists a *-algebra B(X) ⊂ L(X) which contains the identity operator I and all bounded linear operators with finite-dimensional range. The main result is: if each operator U ∈ B(X) with the property U*U = UU* = I has norm one then X is a Hilbert space.

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