scholarly journals Reverse inequalities for the numerical radius of linear operators in Hilbert spaces

2006 ◽  
Vol 73 (2) ◽  
pp. 255-262 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Upper Bounds ◽  
Linear Operators ◽  
Numerical Radius ◽  
Bounded Linear ◽  
The Difference ◽  
Reverse Inequalities

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

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 On Numerical Radius Bounds Involving Generalized Aluthge Transform

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Tao Yan ◽  
Javariya Hyder ◽  
Muhammad Saeed Akram ◽  
Ghulam Farid ◽  
Kamsing Nonlaopon
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Polar Decomposition ◽  
Upper Bounds ◽  
Complex Hilbert Space ◽  
Numerical Radius ◽  
Aluthge Transform ◽  
Bounded Linear

In this paper, we establish some upper bounds of the numerical radius of a bounded linear operator S defined on a complex Hilbert space with polar decomposition S = U ∣ S ∣ , involving generalized Aluthge transform. These bounds generalize some bounds of the numerical radius existing in the literature. Moreover, we consider particular cases of generalized Aluthge transform and give some examples where some upper bounds of numerical radius are computed and analyzed for certain operators.

scholarly journals Additive perturbations and multiplicative perturbations for the core inverse of bounded linear operator in Hilbert space

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6131-6144
Author(s):  
Fapeng Du ◽  
Zuhair Nashed
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Hilbert Spaces ◽  
Upper Bound ◽  
Bounded Linear Operator ◽  
Upper Bounds ◽  
Bounded Linear ◽  
The Core ◽  
Core Inverse

In this paper, we present some characteristics and expressions of the core inverse A# of bounded linear operator A in Hilbert spaces. Additive perturbations of core inverse are investigated under the condition R( ?)?N(A#) = {0} and an upper bound of ||?#-A#|| is obtained. We also discuss the multiplicative perturbations. The expressions of core inverse of perturbed operator T = EAF and the upper bounds of ||T#-A#|| are obtained too.

Matrix mappings and general bounded linear operators on the space bv

2018 ◽  
Vol 68 (2) ◽  
pp. 405-414
Author(s):  
Ivana Djolović ◽  
Katarina Petković ◽  
Eberhard Malkowsky
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Linear Operators ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Hausdorff Measures ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Matrix ◽  
The Difference

Abstract If X and Y are FK spaces, then every infinite matrix A ∈ (X, Y) defines a bounded linear operator LA ∈ B(X, Y) where LA(x) = Ax for each x ∈ X. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y, that is, L ∈ B(X, Y), we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space bv into the spaces ℓ∞, c and c0. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the difference between general bounded linear operators between some sequence spaces and the matrix operators associated with matrix transformations.

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 A New Inequality for Frames in Hilbert Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Bessel Sequences

We obtain a new inequality for frames in Hilbert spaces associated with a scalar and a bounded linear operator induced by two Bessel sequences. It turns out that the corresponding results due to Balan et al. and Găvruţa can be deduced from our result.

Separable Banach lattices on which every bounded linear operator is regular

2011 ◽  
Vol 150 (3) ◽  
pp. 557-560
Author(s):  
A. W. WICKSTEAD
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Positive Operators ◽  
Banach Lattices ◽  
Bounded Linear ◽  
The Difference

AbstractWe give a complete description of those separable Banach lattices E with the property that every bounded linear from E into itself is the difference of two positive operators.

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].

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