Hilbert Space
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.
AbstractAbstract
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.
Sitati IN, Nzimbi BM, Luketero SW, Khalagai JM. "
On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities."
SciencePG journals. 2016;Vol. 1(3 ):56-60.
AbstractIn this paper, we investigate properties of A-self-adjoint operators and other relations on Hilbert spaces. In this
context, A is a self-adjoint and an invertible operator. More results on operator equivalences including similarity, unitary and metric equivalences are discussed. We also investigate conditions under which these classes of operators are self- adjoint and unitary. We finally locate their spectra.
