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Growth Conditions and Decomposable Operators

Published online by Cambridge University Press:  20 November 2018

Mehdi Radjabalipour
Mehdi Radjabalipour*
Affiliation:
University of Toronto, Toronto, Ontario; Dalhousie University, Halifax, Nova Scotia
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Throughout this paper T will denote a bounded linear operator which is defined on a Banach space and whose spectrum lies on a rectifiable Jordan curve J .

The operators having some growth conditions on their resolvents have been the subject of discussion for a long time. Many sufficient conditions have been found to ensure that such operators have invariant subspaces [2 ; 3 ; 7 ; 8 ; 12 ; 13; 14; 21; 27; 28; 29], are S-operators [14], are quasidecomposable [9], are decomposable [4 ; 11], are spectral [7 ; 10 ; 15 ; 17], are similar to normal operators [16 ; 23 ; 25 ; 26], or are normal [15 ; 18 ; 22]. In this line we are going to show that many such operators are decomposable.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1372 - 1379
Copyright
Copyright © Canadian Mathematical Society 1974

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