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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Authors: Ciprian Foias and Allen Tannenbaum
Journal: Proc. Amer. Math. Soc. 101 (1987), 687-692
MSC: Primary 47A20; Secondary 47A45
MathSciNet review: 911034
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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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DOI: https://doi.org/10.1090/S0002-9939-1987-0911034-6
Keywords: Compressed shift, commutant, Hardy spaces
Article copyright: © Copyright 1987 American Mathematical Society