Open AccessWeyl’s theorem holds for algebraically hyponormal operators
Author(s) -
Young Min Han,
Woo Lee
Publication year - 2000
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-00-05741-5
Subject(s) - algorithm , artificial intelligence , annotation , parenthesis , type (biology) , computer science , linguistics , philosophy , biology , ecology
In this note it is shown that if T T is an “algebraically hyponormal" operator, i.e., p ( T ) p(T) is hyponormal for some nonconstant complex polynomial p p , then for every f ∈ H ( σ ( T ) ) f\in H(\sigma (T)) , Weyl’s theorem holds for f ( T ) f(T) , where H ( σ ( T ) ) H(\sigma (T)) denotes the set of analytic functions on an open neighborhood of σ ( T ) \sigma (T) .