Open AccessA Fredholm alternative-like result on power bounded operators
Author(s) -
A. Ülger,
Onur Yavuz
Publication year - 2011
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-0912-68
Subject(s) - mathematics , bounded function , bounded operator , invertible matrix , compact operator , finite rank operator , linear operators , banach space , banach algebra , projection (relational algebra) , pure mathematics , discrete mathematics , operator (biology) , mathematical analysis , biochemistry , chemistry , algorithm , repressor , computer science , transcription factor , extension (predicate logic) , gene , programming language
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