A-almost Similarity

Sitati IN, Nzimbi BM, Luketero SW, Khalagai JM. "Remarks on A-skew-adjoint, A-almost similarity equivalence and other operators in Hilbert space." Pure and Applied Mathematics Journal. 2017;6(3):101-107. AbstractWebsite

Abstract
In this paper, notions of A-almost similarity and the Lie algebra of A-skew-adjoint operators in Hilbert space are introduced. In this context, A is a self-adjoint and an invertible operator. It is shown that A-almost similarity is an equivalence relation. Conditions under which A-almost similarity implies similarity are outlined and in which case their spectra is located. Conditions under which an A-skew adjoint operator reduces to a skew adjoint operator are also given. By relaxing some conditions on normal and unitary operators, new results on A -normal, binormal and A-binormal operators are proved. Finally A-skew adjoint operators are characterized and the relationship between A-self- adjoint and A-skew adjoint operators is given.

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