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On quasi-similarity and w-hyponormal operators

Otieno M. O.

Opuscula Mathematica

2007

Vol. 27, no. 1

73-81

In this paper, it is shown that a Putnam-Fuglede type commutativity theorem holds for w-hyponormal operators, the normal parts of quasi-similar w-hyponormal operators are unitarily equivalent and a w-hyponormal spectral operator is normal.

On intertwining and w-hyponormal operators

Otieno M.O.

Opuscula Mathematica

2005

Vol. 25, no. 2

275-285

Given A, B mem B(H), the algebra of operators on a Hilbert Spaces H, define deltaA,B : B(H) arr B(H) and DeltaA,B : B(H) arr B(H) by deltaA,B(X) = AX - XB and DeltaA,B(X) = AXB - X. In this note, our task is a twofold one. We show firstly that if A and B* are contractions with C.o completely non unitary parts such that X mem ker DeltaA,B, then X mem ker DeltaA*,B*. Secondly, it is shown that if A and B* are w-hyponormal operators such that X mem ker deltaA,B and Y mem ker deltaB,A, where X and Y are quasi-affinities, then A and B are unitarily equivalent normal operators. A w-hyponormal operator compactly quasi-similar to an isometry is unitary is also proved.