TY  - JOUR
ID  - Gao2012
LB  - Gao2012
AU  - Gao, Fugen
AU  - Fang, Xiaochun
TI  - Weyl's theorem for algebraically k-quasiclass A operators
ST  - Weyl's theorem for algebraically k-quasiclass A operators
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 1
SP  - 125
EP  - 135
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.1.125
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.1.125
AB  - If \(T\) or \(T^*\) is an algebraically \(k\)-quasiclass \(A\) operator acting on an infinite dimensional separable Hilbert space and \(F\) is an operator commuting with \(T\), and there exists a positive integer \(n\) such that \(F^n\) has a finite rank, then we prove that Weyl's theorem holds for \(f(T)+F\) for every \(f \in H(\sigma(T))\), where \(H(\sigma(T))\) denotes the set of all analytic functions in a neighborhood of \(\sigma(T)\). Moreover, if \(T^*\) is an algebraically \(k\)-quasiclass \(A\) operator, then \(\alpha\)-Weyl's theorem holds for \(f(T)\). Also, we prove that if \(T\) or \(T^*\) is an algebraically \(k\)-quasiclass \(A\) operator then both the Weyl spectrum and the approximate point spectrum of \(T\) obey the spectral mapping theorem for every \(f \in H(\sigma(T))\).
KW  - algebraically \(k\)-quasiclass \(A\) operator
KW  - Weyl's theorem
KW  - \(\alpha\)-Weyl's theorem
SN  - 1232-9274
ER  -