On the uniqueness of a minimal norm representative of an operator in the commutant of the compressed shift

Foias, Ciprian; Tannenbaum, Allen

doi:10.1090/S0002-9939-1987-0911034-6

On the uniqueness of a minimal norm representative of an operator in the commutant of the compressed shift
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by Ciprian Foias and Allen Tannenbaum PDF

Proc. Amer. Math. Soc. 101 (1987), 687-692 Request permission

Abstract:

In this note we give a new criterion guaranteeing the uniqueness of a minimal norm representative of a bounded linear operator which commutes with a finite multiplicity shift. We moreover give examples which show that if the hypotheses of our theorem are violated then the minimal norm representative may not be unique.

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