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On the Generalized Fuglede-Putnam Theorem
並列摘要
In this paper, we prove the following assertions: (1) If the pair of operators (A, B(superscript *)) satisfies the Fuglede-Putnam Property and S ∈ ker (δ(subscript A, B)) where S ∈ B (H), then we have (The equation is abbreviated) (2) Suppose the pair of operators (A, B(superscript *)) satisfies the Fuglede-Putnam Property. If A^2X=XB^2 and A^3X=XB^3, then AX=XB. (3) Let A, B ∈ B (H) be such that A,B(superscript *) are p-hyponormal. Then for any X ∈ C2, AX-XB ∈ C2 implies A(superscript *)X-XB(superscript *) ∈ C2. (4) Let T, S ∈ B (H) be such that T and S(superscript *) are quasihyponormal operators. If X ∈ B (H) and TX=XS, then T(superscript *)X=XS(superscript *).
並列關鍵字
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