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.

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.

Common spectral properties of linear operators A and B satisfying AkBkAk = Ak+1 and BkAkBk = Bk+1

2019 ◽  
Vol 12 (05) ◽  
pp. 1950084
Author(s):  
Anuradha Gupta ◽  
Ankit Kumar
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Spectral Properties ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

Let [Formula: see text] and [Formula: see text] be two bounded linear operators on a Banach space [Formula: see text] and [Formula: see text] be a positive integer such that [Formula: see text] and [Formula: see text], then [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] have some common spectral properties. Drazin invertibility and polaroidness of these operators are also discussed. Cline’s formula for Drazin inverse in a ring with identity is also studied under the assumption that [Formula: see text] for some positive integer [Formula: see text].

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.

scholarly journals Spectral properties and restrictions of bounded linear operators

2015 ◽  
Vol 6 (2) ◽  
pp. 173-183
Author(s):  
C. Carpintero ◽  
E. Rosas ◽  
J. Rodriguez ◽  
D. Muñoz ◽  
K. Alcalá
Keyword(s):  
Spectral Properties ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

scholarly journals OPERATORS ON BANACH ALGEBRA VALUED FUNCTION SPACES

1992 ◽  
Vol 23 (3) ◽  
pp. 233-238
Author(s):  
JOR-TING CHAN
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Function Spaces ◽  
Linear Operators ◽  
Locally Compact ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Locally Compact Hausdorff Space

Let $S$ be a locally compact Hausdorff space and let $A$ be a Banach algebra. Denote by $C_0(S, A)$ the Banach algebra of all $A$-valued continuous functions vanishing at infinity on $S$. Properties of bounded linear operators on $C_0(S,A)$, like multiplicativity, are characterized by Choy in terms of their representing measures. We study these theorems and give sharper results in certain cases.

Common local spectral properties of bounded linear operators AT and SA such that BSA=ATB

2015 ◽  
Vol 9 ◽  
pp. 183-193
Author(s):  
Abdelaziz Tajmouati ◽  
Abdeslam El Bakkali ◽  
Mohamed Baba Mohamed Ahmed
Keyword(s):  
Spectral Properties ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear
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