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

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Teimourian Rudin; Ghazanfari Amir ghasem

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2021 | Volume:6 | Issue:28 Page(s): 135-143

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Title

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

Author(s)

Teimourian Rudin | Ghazanfari Amir ghasem | Issue Writer Certificate

Keywords

Hadamard product

Operator inequality

Chebyshev inequality

Schwarz inequality

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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APA: Copy

Teimourian, Rudin, & Ghazanfari, Amir ghasem. (2021). SOME GENERALIZATIONS OF CHEBYSHEV TYPE INEQUALITIES INVOLVING THE HADAMARD PRODUCT IN L^p SPACES CONSIST OF OPERATORS VALUE FUNCTIONS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(28 ), 135-143. SID. https://sid.ir/paper/952104/en

Vancouver: Copy

Teimourian Rudin, Ghazanfari Amir ghasem. SOME GENERALIZATIONS OF CHEBYSHEV TYPE INEQUALITIES INVOLVING THE HADAMARD PRODUCT IN L^p SPACES CONSIST OF OPERATORS VALUE FUNCTIONS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;6(28 ):135-143. Available from: https://sid.ir/paper/952104/en

IEEE: Copy

Rudin Teimourian, and Amir ghasem Ghazanfari, “SOME GENERALIZATIONS OF CHEBYSHEV TYPE INEQUALITIES INVOLVING THE HADAMARD PRODUCT IN L^p SPACES CONSIST OF OPERATORS VALUE FUNCTIONS,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 28 , pp. 135–143, 2021, [Online]. Available: https://sid.ir/paper/952104/en

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