# Extension of Euclidean operator radius inequalities

@article{Moslehian2015ExtensionOE,
title={Extension of Euclidean operator radius inequalities},
author={Mohammad Sal Moslehian and Mostafa Sattari and Khalid Shebrawi},
journal={arXiv: Functional Analysis},
year={2015}
}
• Published 31 January 2015
• Mathematics
• arXiv: Functional Analysis
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 $p\geq1$. 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…
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