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
In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal...In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.展开更多
In this paper we initiate a study of covariance and variance for two operators on a Hilbert space. proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy- Schwarz inequality. As...In this paper we initiate a study of covariance and variance for two operators on a Hilbert space. proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy- Schwarz inequality. As for applications of the c-v inequality we provc uniformly the Bernstein-type inequalities and equalities. and show the generalized Heinz-Kato-Furuta-type inequalities and equalities. from which a generalization and sharpening of Reid’s inequlality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given.展开更多
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.
基金Supported by the Education Foundation of Henan Province(2003110006)
文摘In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.
文摘In this paper we initiate a study of covariance and variance for two operators on a Hilbert space. proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy- Schwarz inequality. As for applications of the c-v inequality we provc uniformly the Bernstein-type inequalities and equalities. and show the generalized Heinz-Kato-Furuta-type inequalities and equalities. from which a generalization and sharpening of Reid’s inequlality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given.
