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Continuity of the generalized kernel and range of semi-Fredholm operators

Published online by Cambridge University Press:  04 October 2011

M. Ó Searcóid  and
T. T. West
M. Ó Searcóid
Affiliation:
University College, Dublin
T. T. West
Affiliation:
Trinity College, Dublin
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Extract

Let X denote a Banach space over the complex field ℂ and let B(X) be the Banach algebra of all bounded linear operators on X. If T ε B(X), we write n(T) = dim ker (T) and d(T) = codim T(X). Suppose that Y is a subspace invariant under T; then TY will denote the restriction of T to Y and Y the operator on X/Y defined by

Y: x/Y →(Tx)/Y

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 513 - 522
Copyright
Copyright © Cambridge Philosophical Society 1989

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