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- W1626178545 abstract "To extend the Euclidean operator radius, we define $w_p$ for an $n$-tuples of operators $(T_1,ldots, T_n)$ in $mathbb{B}(mathscr{H})$ by $w_p(T_1,ldots,T_n):= sup_{| x | =1} left(sum_{i=1}^{n}| langle T_i x, x rangle |^p right)^{frac1p}$ for $pgeq1$. We generalize some inequalities including Euclidean operator radius of two operators to those involving $w_p$. Further we obtain some lower and upper bounds for $w_p$. Our main result states that if $f$ and $g$ are nonnegative continuous functions on $left[ 0,infty right) $ satisfying $fleft( tright) gleft(tright) =t$ for all $tin left[ 0,infty right) $, then begin{equation*} w_{p}^{rp}left( A_{1}^{ast }T_{1}B_{1},ldots ,A_{n}^{ast }T_{n}B_{n}right) leq frac{1}{2}leftVert underset{i=1}{overset{n}{sum }}Big( left[ B_{i}^{ast }f^{2}left( leftvert T_{i}rightvert right) B_{i}right] ^{rp}+left[ A_{i}^{ast }g^{2}left( leftvert T_{i}^{ast }rightvert right) A_{i}right] ^{rp}Big)rightVert end{equation*} for all $pgeq 1$, $rgeq 1$ and operators in $ mathbb{B}(mathscr{H})$." @default.
- W1626178545 created "2016-06-24" @default.
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- W1626178545 date "2015-01-31" @default.
- W1626178545 modified "2023-09-27" @default.
- W1626178545 title "Extension of Euclidean operator radius inequalities" @default.
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- W1626178545 hasPublicationYear "2015" @default.
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