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- W2808077692 abstract "We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators. Among other inequalities, it is shown that if ${mathfrak A}$ is a $C^*$-algebra, $T$ is a compact Hausdorff space equipped with a Radon measure $mu$ as a totaly order set, then begin{align*} int_{T} alpha(s) dmu(s)int_{T}alpha(t)(A_tcirc B_t) dmu(t)geqBig{(}int_{T}alpha(t) (A_tm_{r,alpha} B_t) dmu(t)Big{)}circBig{(}int_{T}alpha(s) (A_sm_{r,1-alpha} B_s) dmu(s)Big{)}, end{align*} where $alphain[0,1]$, $rin[-1,1]$ and $(A_t)_{tin T}, (B_t)_{tin T} $ are positive increasing fields in $mathcal{C}(T,mathfrak A)$." @default.
- W2808077692 created "2018-06-21" @default.
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- W2808077692 date "2018-06-15" @default.
- W2808077692 modified "2023-09-27" @default.
- W2808077692 title "Noncommutative Chebyshev inequality involving the Hadamard product" @default.
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