On unitary equivalence of some classes of operators in Hilbert spaces

Citation:
Luketero SW, Khalagai JM. "On unitary equivalence of some classes of operators in Hilbert spaces." International Journal of Statistics and Applied Mathematics. 2020;5(2):35-37.

Abstract:

It is a well-known result in operator theory that whenever two operators are similar then they have equal spectra even though they do not have to belong to the same class of operators. However under a stronger relation of unitary equivalence it can be shown that two unitarily equivalent operators may belong to the same class of operators. In this paper we endeavor to exhibit results on such classes of operators which belong to same class under unitary equivalence.

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