scholarly journals A note on the common spectral properties for bounded linear operators

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4575-4584
Author(s):  
Hassane Zguitti
Keyword(s):  
Banach Spaces ◽  
Spectral Properties ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Common

Let X and Y be Banach spaces, A : X ? Y and B, C : Y ? X be bounded linear operators. We prove that if A(BA)2 = ABACA = ACABA = (AC)2A, then ?*(AC) {0} = ?*(BA)\{0} where ?+ runs over a large of spectra originated by regularities.

scholarly journals Five short lemmas in Banach spaces

2016 ◽  
Vol 32 (1) ◽  
pp. 131-140
Author(s):  
QINGPING ZENG ◽  
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Commutative Diagram ◽  
Spectral Properties ◽  
Linear Operators ◽  
General Question ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Local Spectral Theory

Consider a commutative diagram of bounded linear operators between Banach spaces...with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory.

scholarly journals A spectral radius problem connected with weak compactness

1993 ◽  
Vol 35 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Spectral Radius ◽  
Spectral Properties ◽  
Weak Compactness ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Radius Problem

The asymptotic behaviour has been determined for several natural geometric or topological quantities related to (degrees of) compactness of bounded linear operators on Banach spaces; see for instance [24], [25] and [17]. This paper complements these results by studying the spectral properties of some quantities related to weak compactness.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

scholarly journals Uniqueness of the maximal ideal of operators on the ℓp-sum of ℓ∞n (n ∈ ) for 1 < p < ∞

2016 ◽  
Vol 160 (3) ◽  
pp. 413-421 ◽  
Author(s):  
TOMASZ KANIA ◽  
NIELS JAKOB LAUSTSEN
Keyword(s):  
Banach Space ◽  
Recent Result ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Maximal Ideal ◽  
American Mathematical Society ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Unique Maximal Ideal

AbstractA recent result of Leung (Proceedings of the American Mathematical Society, 2015) states that the Banach algebra ℬ(X) of bounded, linear operators on the Banach space X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓ1 contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓp and X = (⊕n∈$\mathbb{N}$ ℓ1n)ℓp whenever p ∈ (1, ∞).

scholarly journals Locally compact semi-algebras generated by a commuting operator family

1994 ◽  
Vol 17 (4) ◽  
pp. 717-724
Author(s):  
N. R. Nandakumar ◽  
Cornelis V. Vandermee
Keyword(s):  
Spectral Properties ◽  
Linear Operators ◽  
Finite Collection ◽  
Operator Family ◽  
Locally Compact ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Local Compactness

Conditions are provided for the local compactness of the closed semi-algebra generated by a finite collection of commuting bounded linear operators with equibounded iterates in terms of their joint spectral properties.

scholarly journals On Riesz operators

1969 ◽  
Vol 16 (3) ◽  
pp. 227-232 ◽  
Author(s):  
J. C. Alexander
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Operators ◽  
Image Position ◽  
Schauder’S Theorem

In (4) Vala proves a generalization of Schauder's theorem (3) on the compactness of the adjoint of a compact linear operator. The particular case of Vala's result that we shall be concerned with is as follows. Let t1 and t2 be non-zero bounded linear operators on the Banach spaces Y and X respectively, and denote by 1T2 the operator on B(X, Y) defined by

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