On the uniqueness of a minimal norm representative of an operator in the commutant of the compressed shift-Reference-Cited by-同舟云学术

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

Published:1987 Issue:4 Volume:101 Page:687-692
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Foias Ciprian,Tannenbaum Allen

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1987-101-04/S0002-9939-1987-0911034-6/S0002-9939-1987-0911034-6.pdf

Reference16 articles.

1. Infinite Hankel matrices and generalized Carathéodory-Fejér and I. Schur problems;Adamjan, V. M.;Funkcional. Anal. i Prilo\v{z}en.,1968

2. \bysame, Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem, Math. USSR Sb. 15 (1971), 31-73.

3. On intertwining dilations. IV;Arsene, Grigore;Tohoku Math. J. (2),1978

4. The extended spectrum of completely non-unitary contractions and the spectral mapping theorem;Foiaş, C.;Studia Math.,1966

5. On the Nehari problem for a certain class of 𝐿^{∞}-functions appearing in control theory;Foias, Ciprian;J. Funct. Anal.,1987

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