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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Fuglede-Putnam theorem and a generalization of Barría’s lemma
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by Toshihiro Okuyama and Keiichi Watanabe PDF
Proc. Amer. Math. Soc. 126 (1998), 2631-2634 Request permission

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
  • MR Author ID: 216208
  • Received by editor(s): October 19, 1995
  • Received by editor(s) in revised form: January 27, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • 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