Full Length Research Paper
Abstract
Let T be a contraction on a complex Hilbert space H, let be the local spectrum of
at
, and let
be the local unitary spectrum of T at ;
. We show that if
is of Lebesgue measure zero, then
, where
is the unitary part of
in the canonical decomposition of H with respect to T.
Key words: Hilbert space, contraction, local spectrum.
Copyright © 2024 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0