On unitary equivalence and almost similarity of some classes of operators in Hilbert spaces

Abstract

In operator theory, it is a well-known fact that two similar operators have equal spectra even if they do not 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 our task is to show some results on such operators which belong to the same class and not only unitary equivalence but also under isometric equivalence. We also endeavor to extend this consideration to almost similarity of operators.