D, Sukumar and Veeramani, S
(2017)
Level sets of (p,ep)outer generalized pseudo spectrum.
Journal of Analysis.
pp. 114.
ISSN 09713611
(In Press)
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Abstract
Let A be a complex Banach algebra with unit e. Let p be a non trivial idempotent element in A and ε>0. For a∈A, it is proved that the interior of the level set of (p,e−p)−ε pseudo spectrum of a is empty in the unbounded component of (p,e−p) resolvent set of a. An example is constructed to show that the condition ‘unbounded component’ can not be dropped. Further, it is proved this ‘unbounded component’ can be dropped in the case when A is B(X) where X is a complex uniformly convex Banach space. That is, if T∈B(X) then interior of the level set of (p,I−p)−ε pseudo spectrum is empty in (p,I−p) resolvent set of T.
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