A fredholm alternative-like result on power bounded operators

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Ülger, Ali and Yavuz, Onur (2011) A fredholm alternative-like result on power bounded operators. Turkish Journal of Mathematics, 35 (3). pp. 473-478. ISSN 1300-0098

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Abstract

Let X be a complex Banach space and T : X -> X be a power bounded operator, i.e., sup(n >= 0) parallel to T(m)parallel to < infinity. We write B(X) for the Banach algebra of all bounded linear operators on X. We prove that the space Ran(I - T) is closed if and only if there exist a projection theta is an element of B(X) and an invertible operator R is an element of B(X) such that I - T = theta R = R theta. This paper also contains some consequences of this result.
Item Type: Article
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Onur Yavuz
Date Deposited: 18 Nov 2011 22:06
Last Modified: 30 Jul 2019 14:33
URI: https://research.sabanciuniv.edu/id/eprint/17463

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