A fredholm alternative-like result on power bounded operators

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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Official URL: http://dx.doi.org/10.3906/mat-0912-68


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
ID Code:17463
Deposited By:Onur Yavuz
Deposited On:18 Nov 2011 22:06
Last Modified:30 Jul 2019 14:33

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