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Proceedings of the American Mathematical Society

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

 

 

The Fuglede-Putnam theorem
and a generalization of Barría's lemma


Authors: Toshihiro Okuyama and Keiichi Watanabe
Journal: Proc. Amer. Math. Soc. 126 (1998), 2631-2634
MSC (1991): Primary 47A62, 47A99; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9939-98-04355-X
MathSciNet review: 1451824
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$ and $B$ be bounded linear operators, and let $C$ be a partial isometry on a Hilbert space. Suppose that (1) $CA=BC$, (2) $\|A\|\ge \|B\|$, (3) $(C^*C)A=A(C^*C)$ and (4) $C(\|A\|^2-AA^*)^{1/2}=0$. Then we have $CA^*=B^*C$.


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Additional Information

Toshihiro Okuyama
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-21, Japan
Address at time of publication: Tsuruoka Minami Highschool, 26-31 Wakaba-cho, Tsuruoka Yamagata-ken 997-0037, Japan
Email: wtnbk@scux.sc.niigata-u.ac.jp

Keiichi Watanabe
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-21, Japan
Address at time of publication: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

DOI: https://doi.org/10.1090/S0002-9939-98-04355-X
Received by editor(s): October 19, 1995
Received by editor(s) in revised form: January 27, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society