Let T be an operator on a separable Hilbert space H and T = U｜T｜ be the polar decomposition. T is said to be log-ω-hyponormal if log ｜~T｜ ≥ log｜T｜≥ log ｜~T^＊｜. In this paper we prove that the point spectru...Let T be an operator on a separable Hilbert space H and T = U｜T｜ be the polar decomposition. T is said to be log-ω-hyponormal if log ｜~T｜ ≥ log｜T｜≥ log ｜~T^＊｜. In this paper we prove that the point spectrum of T is equal to its joint point spectrum if T is log-ω-hyponormal. We also prove that a log-ω-hyponormal operator is normaloid, i.e., r（T） =｜｜T｜｜. Finally, we obtain Putnam＇s theorem for log-ω-hyponormal operators.展开更多
The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectr...The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.展开更多
It is known that the square of a ω-hyponormal operator is also ω-hyponormal. For any 0〈 p 〈 1, there exists a special invertible operator such that all of its integer powers are all p - ω-hyponormal. In this arti...It is known that the square of a ω-hyponormal operator is also ω-hyponormal. For any 0〈 p 〈 1, there exists a special invertible operator such that all of its integer powers are all p - ω-hyponormal. In this article, the author introduces the class of （s, p） -ω-hyponormal operators on the basis of the class of p- ω-hyponormal operators. For s 〉0, 0 〈 p 〈 1, the author gives a characterization of （s,p） -ω-hyponormal operatots; the author shows that all integer powers of special （s, p） -ω-hyponormal operators are （s,p） -ω-hyzponormal.展开更多
文摘Let T be an operator on a separable Hilbert space H and T = U｜T｜ be the polar decomposition. T is said to be log-ω-hyponormal if log ｜~T｜ ≥ log｜T｜≥ log ｜~T^＊｜. In this paper we prove that the point spectrum of T is equal to its joint point spectrum if T is log-ω-hyponormal. We also prove that a log-ω-hyponormal operator is normaloid, i.e., r（T） =｜｜T｜｜. Finally, we obtain Putnam＇s theorem for log-ω-hyponormal operators.
文摘The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.
基金Science Foundation of Ministry of Education of China
文摘It is known that the square of a ω-hyponormal operator is also ω-hyponormal. For any 0〈 p 〈 1, there exists a special invertible operator such that all of its integer powers are all p - ω-hyponormal. In this article, the author introduces the class of （s, p） -ω-hyponormal operators on the basis of the class of p- ω-hyponormal operators. For s 〉0, 0 〈 p 〈 1, the author gives a characterization of （s,p） -ω-hyponormal operatots; the author shows that all integer powers of special （s, p） -ω-hyponormal operators are （s,p） -ω-hyzponormal.
