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
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.
