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Fuglede-putnam theorem for (p, k)-quasihyponormal and class (Y )operators
(Maltepe Üniversitesi, 2009) Bakir, Aissa Nasli
Let A and B be normal operators on a complex separable Hilbert space H. The equation AX = XB implies A ?X = XB? for some operatorX on H ino itself is known as the familiar Fuglede-Putnam theorem. An operator A ? B(H) is said to be log-hyponormal if A is invertible and log(A ?A) ? log(AA? ), class (Y ) if there exist ? ? 1 and k? > 0 such that |AA? ? A ?A| ? ? k 2 ? (A ? ?) ? (A ? ?) for all ? ? C, dominant if ran(A ? ?) ? ran(A ? ?) ? for all ? ? ?(A) where ?(A) denotes the spectrum ofA. A is called (p, k)-quasihyponormal if A ?k ((A ?A) p ? (AA? ) p )A k ? 0, k ? N, 0 < p ? 1. In this talk, we’ll give an extension of Fuglede-Putnam’s result to the case when either 1) A is log-hyponormal operator and B ? is a class (Y ) operator 2) A is (p, k)-quasihyponormal operator with ker A ? ker A ? and B ? is dominant. Other results are also given.