Generalization of Fuglede-Putnam Theorem to (p, q)−Quasiposinormal Operator and (p, q)− Co-posinormal Operator
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Abstract
In this paper we generalize the Fuglede-Putnam theorem to non-normal operators to posinormal operator and co-posinormal operators. Also we prove this theorem to supra class posinormal operators (called supraposinormal operator) and co-supra class posinormal operators (called cosupraposinormal operator).
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References
[1] Hichem M. Mortad: Yet More Versions of The Fuglede-Putnam Theorem, Glasgow Mathematical Journal Trust (2009) 473-480.
[2] Dixmier J: Les Algebres d'operateurs dans L'espace Hilberien (Algebres de Von Neumann, Gauthier Villars, Paris. MR 20, 1234. Second Edition (1969).
[3] S. K. Berberian: Extensions of theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 71 (1978) No. 1, 113-114.
[4] H. C. Rhaly Jr.: Posinormal Operators, J. Math. Soc. Japan 46 (4) (1994) 587-605.
[5] Mi Young Lee and Sang Hun Lee: On (p, k)-Quasiposinormal Operators, J. Appl. Math. & Computing Vol. 19 (2005) No. 1-2, 573 - 578.
[6] John B. Conway: A course in Functional Analysis, McGraw Hill New yourk (1991) (2nd edition).
[7] W. Rudin: Functional Analysis, Springer-Verlag, New York (1990) (2nd edition).
[8] F. Hansen : An Operator Inequality, Math. Ann. 246 (1980) 249-250.
[9] E. Heinz: Beitrge zur Strungstheorie der Spektralzerlegung,Math. Ann.123 (1951) 415-438.
[10] K. Lowner: uber monotone Matrixfunktionen, Math. Z. 38 (1934) 177-216.
[11] Loenath Debnath and Piotr Mikusinski: Introduction to Hilbert Spaces with Applications, Elsevier Academic Press (2005) (3rd edition).