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

Author(s): Toshihiro Okuyama; Keiichi Watanabe
Journal: Proc. Amer. Math. Soc. 126 (1998), 2631-2634.
MSC (1991): Primary 47A62, 47A99; Secondary 47B20
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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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J. Barría, The commutative product $V^*_1V_2=V_2V^*_1$ for isometries $V_1$ and $V_2$, Indiana Univ. Math. J. 28 (1979), 581-585. MR 80h:47021

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S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175-182. MR 21:6548

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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: 10.1090/S0002-9939-98-04355-X
PII: S 0002-9939(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
Copyright of article: Copyright 1998, American Mathematical Society

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