Generalized α-Browder's and Generalized α-Weyl's Theorems for Banach Space

M. H. M. RASHID^1,

¹Department of Mathematics& Statistics, Faculty of Science P.O.Box(7), Mu'tah University, Al-Karak, Jordan

Cite this paper:
M. H. M. RASHID. Generalized α-Browder's and Generalized α-Weyl's Theorems for Banach Space. Turkish Journal of Analysis and Number Theory. 2016; 4(5):146-154. doi: 10.12691/tjant-4-5-5

Abstract

In this paper, we give necessary and sufficient conditions for a Banach space T to satisfy the generalized α-Browder’s theorem. We also prove that the spectral mapping theorem holds for the left Drazin invertible and for analytic functions on a neighborhood of σ(T). As applications, we show that if T^* is algebraically ωF(p,r,q) for each p,r>0 and q≥1, or if T^* is algebraically quasi-class A, then the generalized α-Weyl’s theorem hold for f(T), where f∈Hol(σ(T)), the space of functions analytic on an open neighborhoods of σ(T).

Keywords:
Weyl’s theorem α-Weyl’s theorem generalized α-Weyl’s theorem α-Browder’s theorem generalized α-Browder’s theorem reduction -isoloid reduced subspace

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