scholarly journals Spectral properties of tensor products of linear operators. I

1978 ◽  
Vol 235 ◽  
pp. 75-75 ◽  
Author(s):  
Takashi Ichinose
Keyword(s):  
Spectral Properties ◽  
Tensor Products ◽  
Linear Operators

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.

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.

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].

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