Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T16:52:58.973Z Has data issue: false hasContentIssue false

YET MORE VERSIONS OF THE FUGLEDE–PUTNAM THEOREM*

Published online by Cambridge University Press:  01 September 2009

MOHAMMED HICHEM MORTAD*
Affiliation:
Département de Mathématiques, Université d'Oran (Es-senia), B.P. 1524, El Menouar, Oran 31000, Algeria e-mail: [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give two types of generalisation of the well-known Fuglede–Putnam theorem. The paper is ‘spiced up’ with some examples and applications.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Barría, J., The commutative product V 1*V 2 = V 2V 1* for isometries V 1 and V 2, Indiana Univ. Math. J. 28 (1979), 581585.CrossRefGoogle Scholar
2.Berberian, S. K., Note on a theorem of Fuglede and Putnam, Proc. Am. Math. Soc. 10 (1959), 175182.CrossRefGoogle Scholar
3.Berberian, S. K., Extensions of a theorem of Fuglede and Putnam, Proc. Am. Math. Soc. 71/1 (1978), 113114.CrossRefGoogle Scholar
4.Conway, J. B., A course in functional analysis, 2nd ed. (Springer-Verlag, New York, 1990).Google Scholar
5.Embry, M. R., Similarities involving normal operators on Hilbert space, Pacif. J. Math. 35/2 (1970), 331336.CrossRefGoogle Scholar
6.Fuglede, B., A commutativity theorem for normal operators, Proc. Natl. Acad. Sci. 36 (1950), 3540.CrossRefGoogle ScholarPubMed
7.Furuta, T., On relaxation of normality in the Fuglede–Putnam theorem, Proc. Am. Math. Soc. 77 (1979), 324328.CrossRefGoogle Scholar
8.Furuta, T., Invitation to linear operators: From matrices to bounded linear operators on a Hilbert space (CRC Press, London, 2002).Google Scholar
9.Halmos, P. R., A Hilbert space problem book (Springer-Verlag, New York, 1974).CrossRefGoogle Scholar
10.Jeon, I. H., Kim, S. H., Ko, E. and Park, J. E., On positive-normal operators, Bull. Korean Math. Soc. 39/1 (2002), 3341.CrossRefGoogle Scholar
11.Mortad, M. H., An application of the Putnam–Fuglede theorem to normal products of self-adjoint operators, Proc. Am. Math. Soc. 131/10 (2003), 31353141.CrossRefGoogle Scholar
12.Mortad, M. H., On some product of two unbounded self-adjoint operators, submitted.Google Scholar
13.Okuyama, T. and Watanabe, K., The Fuglede–Putnam theorem and a generalization of Barría's Lemma, Proc. Am. Math. Soc. 126/9 (1998), 26312634.CrossRefGoogle Scholar
14.Putnam, C. R., On normal operators in Hilbert space, Am. J. Math. 73 (1951), 357362.CrossRefGoogle Scholar
15.Radjabalipour, M., An extension of Putnam–Fuglede theorem for hyponormal operators, Math. Zeit. 194/1 (1987), 117120.CrossRefGoogle Scholar
16.Rhaly, H. C. Jr, Posinormal operators, J. Math. Soc. Jpn. 46/4 (1994), 587605.CrossRefGoogle Scholar
17.Rosenblum, M., On a theorem of Fuglede and Putnam, J. Lond. Math. Soc. 33 (1958), 376377.CrossRefGoogle Scholar
18.Rudin, W., Functional analysis, 2nd ed. (McGraw-Hill, Singapore, 1991).Google Scholar
19.Stampfli, J. G., Wadhwa, B. L., An asymmetric Putnam–Fuglede theorem for dominant operators, Indiana Univ. Math. J. 25/4 (1976), 359365.CrossRefGoogle Scholar
20.Stochel, J., An asymmetric Putnam-Fuglede theorem for unbounded operators, Proc. Am. Math. Soc. 129/8 (2001), 22612271.CrossRefGoogle Scholar
21.Young, N., An introduction to Hilbert space (Cambridge University Press, Cambridge, 1988).CrossRefGoogle Scholar