Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418318 | Journal of Mathematical Analysis and Applications | 2014 | 13 Pages |
Abstract
We establish several operator extensions of the Chebyshev inequality. The main version deals with the Hadamard product of Hilbert space operators. More precisely, we prove that if A is a Câ-algebra, T is a compact Hausdorff space equipped with a Radon measure μ, α:Tâ[0,+â) is a measurable function and (At)tâT, (Bt)tâT are suitable continuous fields of operators in A having the synchronous Hadamard property, thenâ«Tα(s)dμ(s)â«Tα(t)(AtâBt)dμ(t)â¥(â«Tα(t)Atdμ(t))â(â«Tα(s)Bsdμ(s)). We apply states on Câ-algebras to obtain some versions related to synchronous functions. We also present some Chebyshev type inequalities involving the singular values of positive nÃn matrices. Several applications are given as well.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mohammad Sal Moslehian, Mojtaba Bakherad,