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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let and
be bounded linear operators, and let
be a partial isometry on a Hilbert space. Suppose that (1)
, (2)
, (3)
and (4)
. Then we have
.
- 1.
J. Barría, The commutative product
for isometries
and
, Indiana Univ. Math. J. 28 (1979), 581-585. MR 80h:47021
- 2. S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175-182. MR 21:6548
- 3. J. B. Conway, A Course in Functional Analysis (2nd ed.), Springer-Verlag, New York, 1990. MR 91e:46001
- 4. B. Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. 36 (1950), 35-40. MR 11:371c
- 5. T. Furuta, On relaxation of normality in the Fuglede-Putnam theorem, Proc. Amer. Math. Soc. 77 (1979), 324-328. MR 80i:47037
- 6. P. R. Halmos and L. J. Wallen, Powers of partial isometries, J. Math. Mech. 19 (1970), 657-663. MR 40:4801
- 7.
R. L. Moore, D. D. Rogers and T. T. Trent, A note on intertwining
-hyponormal operators, Proc. Amer. Math. Soc. 83 (1981), 514-516. MR 82j:47033
- 8. C. R. Putnam, On normal operators in Hilbert space, Amer. J. Math. 73 (1951), 357-362. MR 12:717f
- 9. J. G. Stampfli and B. L. Wadhwa, On dominant operators, Monatsh. Math. 84 (1977), 143-153. MR 56:16428
- 10. K. Takahashi, On the converse of the Fuglede-Putnam theorem, Acta. Sci. Math. 43 (1981), 123-125. MR 82g:47018
- 11. T. Yoshino, Remark on the generalized Fuglede-Putnam theorem, Proc. Amer. Math. Soc. 95 (1985), 571-572. MR 87i:47034
Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A62, 47A99, 47B20
Retrieve articles in all journals with MSC (1991): 47A62, 47A99, 47B20
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