Browder’s Theorem For Totally Posinormal Operators
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Date
2024-04-08
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Abstract
In our study we consider a higher class of Hilbert space operators, Posinormal operators introduced by
C.Rhaly(1992).The purpose of this paper is to prove that if A is a Totally Posinormal operator such
that σ(A − λI)|M = 0 ⟹ (A − λI) |M = 0 for every M ∈ Lat(A) and satisfies property(ab),then A satisfies
Browder's theorem and generalized Browder’s theorem. We shall also prove that, if N is a nilpotent operator
such that AN = NA,then Browder’s theorem holds for A + N.