A note on quasi-similarity of operators in Hilbert spaces
Date
2015Author
Sitati, Isaiah N
Musundi, Sammy W
Nzimbi, Bernard M
Kikete, W. Dennis
Type
ArticleLanguage
enMetadata
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In this paper we introduce the notion of Quasi-similarity of bounded linear operators in Hilbert Spaces. We do so by defining a quasi- affinity from one Hilbert Space H to K. Some results on quasi- affinities are also discussed. It has already been shown that on a finite dimensional Hilbert Space, quasi similarity is an equivalence relation that is; it is reflexive, symmetric and also transitive. Using the definition of commutants of two operators, we give an alternative result to show that quasi similarity is an equivalence relation on an infinite dimensional Hilbert Space. Finally, we establish the relationship between quasi similarity and almost similarity equivalence relations in Hilbert Spaces using hermitian and normal operators.
Citation
International Mathematical Archive, vol.6 No.7 2015Rights
Attribution-NonCommercial-ShareAlike 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-sa/3.0/us/Collections
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