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Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces

Mesbah Nadia, Messaoudene Hadia, Alharbi Asma

Demonstratio Mathematica

2021

Vol. 54, nr 1

318--325

Let be a complex Hilbert space and B(H) denotes the algebra of all bounded linear operators acting on H. In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators (A, B) ∈ B(H) × B(H) satisfying: ∥ AX – XB − I∥ ≥ 1, for all X ∈ B(H). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.

New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal

Messaoudene Hadia, Mesbah Nadia

Demonstratio Mathematica

2021

Vol. 54, nr 1

311--317

A new class of operators, larger than ∗ -finite operators, named generalized ∗ -finite operators and noted by GF∗ (H) is introduced, where: GF∗ (H) = {(A, B) ∈ B(H) × B(H) : ∥TA - BT∗ - λI∥ ≥ ∣λ∣, ∀λ ∈ C, ∀T ∈ B(H)}. Basic properties are given. Some examples are also presented.

Investigating the numerical range and q-numerical range of non square matrices

Aretaki A, Maroulas J.

Opuscula Mathematica

2011

Vol. 31, no. 3

303-315

A presentation of numerical ranges for rectangular matrices is undertaken in this paper, introducing two different definitions and elaborating basic properties. Further, we extend to the q-numerical range.

A note Gateaux differentials of hermitian elements in Banach algebras

Herzog G., Schmoeger C.

Demonstratio Mathematica

2008

Vol. 41, nr 4

909-913

Let A be a complex unital Banach algebra with unit 1. If a is an element of A is hermitian then we show that [...] and we give a proof of an inequality due to J. Nieto.

Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces

Dragomir S.

Demonstratio Mathematica

2007

Vol. 40, nr 2

411-417

In this paper various inequalities between the operator norm and its numerical radius are provided. For this purpose, we employ some classical inequalities for vectors in inner product spaces due to Buzano, Goldstein-Ryff-Clarke, Dragomir-Sandor and the author.

Finite operators

Mecheri S.

Demonstratio Mathematica

2002

Vol. 35, nr 2

357-366