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Takayuki Furuta 《Proceedings of the American Mathematical Society》1996,124(10):3071-3075
We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.
2.
-hyponormal operators are subscalar Lin Chen Ruan Yingbin Yan Zikun 《Proceedings of the American Mathematical Society》2003,131(9):2753-2759
We prove that if are injective, then is subscalar if and only if is subscalar. As corollaries, it is shown that -hyponormal operators and log-hyponormal operators are subscalar; also w-hyponormal operators with Ker Kerand their generalized Aluthge transformations are subscalar.
3.
-hyponormality is not translation-invariantIn this note we provide an example of a semi-hyponormal Hilbert space operator for which is not -hyponormal for some and all .
4.
Eungil Ko 《Proceedings of the American Mathematical Society》2000,128(3):775-780
In this paper we show that -hyponormal operators with are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.
5.
We prove that for every -hyponormal operator there corresponds a hyponormal operator such that and have ``equal spectral structure". We also prove that every -hyponormal operator is subdecomposable. Then some relevant quasisimilarity results are obtained, including that two quasisimilar -hyponormal operators have equal essential spectra.
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