SOME GENERALIZATIONS OF CHEBYSHEV TYPE INEQUALITIES INVOLVING THE HADAMARD PRODUCT IN L^p SPACES CONSIST OF OPERATORS VALUE FUNCTIONS

Subject Areas : Statistics

Rudin  Teimourian ¹ (Department of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, Iran.)
Amir ghasem  Ghazanfari ² (Department of Mathematics Lorestan University P. O. Box 465, Khoramabad, Iran.)

Received: 2019-09-11 Accepted : 2020-01-09 Published : 2021-02-19

Keywords: نامساوی عملگری, نامساوی چبیشف, ضرب هادامارد, نامساوی شوارتس,

Abstract :

Let B(H) denotes the C*-algebra of all bounded linear operators on a complex Hilbert space H together with the operator norm. Suppose A is a Banach *- subalgebra of B(H) , Ω a compact Hausdorff space equipped with a Radon measure μ and α:Ω→[0,1] is an integrable function. We first introduce the space L^p consists of all operator-valued functions from Ω to A which have finite norm related to a L^p-norm. Next, it is proved that if p and q are conjugate exponents, for every two elements belongs to L^p and L^q with almost synchronous property for the Hadamard product, then we will have a new operator Chebyshev type inequality involving the Hadamard product.Also using some properties of positive linear functional "tr", we introduce a semi-inner product for square integrable functions of operators in L^2. Using the obtained results, we prove the Schwarz and Chebyshev type inequalities dealing with the Hadamard product.

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