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- W4300792004 abstract "In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present begin{align*} w_{p}^{p}(A_{1}^{*}T_{1}B_{1},...,A_{n}^{*}T_{n}B_{n})leqfrac{n^{1-frac{1}{r}}}{2^{frac{1}{r}}}Big|sum_{i=1}^{n}[B_{i}^{*} f^{2}(|T_{i}|)B_{i}]^{rp}+[A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i}]^{rp}Big|^{frac{1}{r}} -inf_{|x|=1}eta(x), end{align*} where $T_{i}, A_{i}, B_{i} in {mathbb B}({mathscr H}),,(1leq ileq n)$, $f$ and $g$ are nonnegative continuous functions on $[0, infty)$ satisfying $f(t)g(t)=t$ for all $tin [0, infty)$, $p, rgeq 1$, $Nin {mathbb N}$ and begin{align*} eta(x)= frac{1}{2}sum_{i=1}^{n}sum_{j=1}^{N} Big(sqrt[2^{j}]{ langle (A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i})^{p}x, xrangle^{2^{j-1}-k_{j}} langle (B_{i}^{*} f^{2}(|T_{i}|)B_{i})^{p}x, xrangle^{k_j}}quad-sqrt[2^{j}]{ langle (B_{i}^{*}f^{2}(|T_{i}|)B_{i})^{p}x, xrangle^{k_{j}+1} langle (A_{i}^{*} g^{2}(|T_{i}^{*}|)A_{i})^{p}x, xrangle^{2^{j-1}-k_{j}-1}}Big)^{2}. end{align*}" @default.
- W4300792004 created "2022-10-04" @default.
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- W4300792004 date "2018-05-19" @default.
- W4300792004 modified "2023-09-30" @default.
- W4300792004 title "Further refinements of generalized numerical radius inequalities for Hilbert space operators" @default.
- W4300792004 doi "https://doi.org/10.48550/arxiv.1805.07596" @default.
- W4300792004 hasPublicationYear "2018" @default.
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