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  1 - SOME GENERALIZATIONS OF CHEBYSHEV TYPE INEQUALITIES INVOLVING THE HADAMARD PRODUCT IN L^p SPACES CONSIST OF OPERATORS VALUE FUNCTIONS
  Rudin Teimourian Amir ghasem Ghazanfari
  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 More

  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. Manuscript profile