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
The goal of this paper is to establish the relations between general Bernstein and Nikol＇skii type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a ...The goal of this paper is to establish the relations between general Bernstein and Nikol＇skii type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol＇skii type inequality is found.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.
基金Supported by the National Science Foundation of China(Grant 90818020, 60874029)
文摘The goal of this paper is to establish the relations between general Bernstein and Nikol＇skii type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol＇skii type inequality is found.
基金Supported by Scientific Program of Department of Education of Jiangxi Province of China(GJJ150894)National Natural Science Foundation of China(61662037)
文摘In this paper we establish L^q inequalities for polynomials, which in particular yields interesting generalizations of some Zygmund-type inequalities.
