Generalized Weyl's theorem and hyponormal operators
2004 ◽
Vol 76
(2)
◽
pp. 291-302
◽
Keyword(s):
AbstractLet T be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of T is the set σBW(T) of all λ ∈ Сsuch that T − λI is not a B-Fredholm operator of index 0. Let E(T) be the set of all isolated eigenvalues of T. The aim of this paper is to show that if T is a hyponormal operator, then T satisfies generalized Weyl's theorem σBW(T) = σ(T)/E(T), and the B-Weyl spectrum σBW(T) of T satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.
1996 ◽
Vol 38
(1)
◽
pp. 61-64
◽
1997 ◽
Vol 39
(2)
◽
pp. 217-220
◽
2015 ◽
Vol 17
(05)
◽
pp. 1450042
1998 ◽
Vol 220
(2)
◽
pp. 760-768
◽
2013 ◽
Vol 59
(1)
◽
pp. 163-172
2002 ◽
Vol 66
(3)
◽
pp. 425-441
◽