Abstract
The following problem was posed by D. A. Herrero in[7]: “Is the multiplicity of the commutant of operators a quasisimilarity invariant?”. Studying this question it is shown that this multiplicity is constant, actually, it is 1, in the quasisimilarity orbits of normal operators, C - contractions, weak contractions and of isometries whose completely non-° unitary parts are of finite multiplicity. Finally, an operator T is constructed, with commutant of infinite multiplicity, so that T is “close” to the quasisimilarity orbit of the unilateral shift of infinite multiplicity.
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