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1.
We analyze the notion of Bishop's property () to obtain some new concepts. We describe some conditions in terms of these concepts for an operator to have its essential spectrum (spectrum) contained in the essential spectrum (spectrum) of every operator quasisimilar to it. A subfamily of such operators is proved to be dense in .
2.
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.
3.
In 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.
陈剑岚 《数学的实践与认识》2008,38(22)
引进亚控制算子的概念,通过算子谱的精密结构的分析,给出拟相似亚控制算子的本质谱相等的若干条件,所得结果改进和发展了Williams L R的有关结果. 相似文献
6.
本文研究两个拟相似算子的右本质谱之间的相交关系.通过引进RT类算子的概念,利用算子谱的精密结构的分析方法,得到一个算子的右本质谱的连通分支与另一个拟相似算子的右本质谱相交的充分和必要条件. 相似文献
7.
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.
8.
Stanislav Shkarin 《Proceedings of the American Mathematical Society》2008,136(5):1659-1670
It is proved that for any separable infinite dimensional Banach space , there is a bounded linear operator on such that satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that satisfies the Kitai criterion for certain backward weighted shifts .
9.
The presence of a modulus function on a Banach algebra gives rise to tensor product norms analogous to the greatest cross‐norm and allows us to extend the Waelbroeck functional calculus. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.