On the Generalized Fuglede-Putnam Theorem

M. H. M. Rashid ； M. S. M. Noorani ； A. S. Saari

《Tamkang Journal of Mathematics》 39卷3期 (2008/09) Pp. 239-246

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 *).