@Article{Gao2012,
author = "Gao, Fugen and Fang, Xiaochun",
title = "Weyl's theorem for algebraically k-quasiclass A operators",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "1",
pages = "125--135",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.1.125",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.1.125",
abstract = "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 \(f \in H(\sigma(T))\).",
keywords = "algebraically \(k\)-quasiclass \(A\) operator, Weyl's theorem, \(\alpha\)-Weyl's theorem",
issn = "1232-9274"
}