Weyl’s Theorem for Algebraically Class A(s, t) Operators

In this study, we show that Weyl’s theorem holds for algebraically class A (s, t) operator acting on Hilbert space. We prove: (i) Weyl’s theorem holds for f (T) for every f belongs to holomorphic function of spectrum of T; (ii) generalized Weyl’s theorem holds for T; (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.