## 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 $CA^*=B^*C$.## References

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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