Equivalence constants for the $l_p$-norms and the $l_q$-symmetric multilinear operator norms of vectors in $\mathbb{C}^n$

Sung Guen Kim

doi:10.4134/CKMS.c190224

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2020; 35(2): 565-570

Online first article December 18, 2019 Printed April 30, 2020

https://doi.org/10.4134/CKMS.c190224

Equivalence constants for the $l_p$-norms and the $l_q$-symmetric multilinear operator norms of vectors in $\mathbb{C}^n$

Sung Guen Kim

Kyungpook National University

Abstract

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Abstract

We investigate the best equivalence constants for the $l_p$-norms and the $l_q$-symmetric multilinear operator norms of vectors in $\mathbb{C}^n$ which are induced by symmetric $n$-linear forms. In this paper, we provides estimates which are either best possible or close to best possible.

Keywords: Equivalence constants for certain norms on $\mathbb{C}^n$

MSC numbers: Primary 46A22