Three kinds of numerical indices of a Banach space II

Sung Guen Kim

doi:10.2989/16073606.2015.1068236

Three kinds of numerical indices of a Banach space II

Sung Guen Kim

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2 Scopus citations

Abstract

For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index (Formula presented.) (E), the symmetric multilinear numerical index (Formula presented.) (E) and the polynomial numerical index (Formula presented.) (E). First we show that (Formula presented.) (E**) ≤ (Formula presented.) (E) for I=m, s and present some inequalities among (Formula presented.) (E), (Formula presented.) (E) and (Formula presented.) (E). We also prove that if E is a strictly convex Banach space, then (Formula presented.) (E)=0 for every k ≥ 2.

Original language	English
Pages (from-to)	153-166
Number of pages	14
Journal	Quaestiones Mathematicae
Volume	39
Issue number	2
DOIs	https://doi.org/10.2989/16073606.2015.1068236
State	Published - 31 Mar 2016

Keywords

homogeneous polynomials
multil̄inear mappings
numerical index
Numerical radius
symmetric multilinear mappings

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10.2989/16073606.2015.1068236

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title = "Three kinds of numerical indices of a Banach space II",

abstract = "For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index (Formula presented.) (E), the symmetric multilinear numerical index (Formula presented.) (E) and the polynomial numerical index (Formula presented.) (E). First we show that (Formula presented.) (E**) ≤ (Formula presented.) (E) for I=m, s and present some inequalities among (Formula presented.) (E), (Formula presented.) (E) and (Formula presented.) (E). We also prove that if E is a strictly convex Banach space, then (Formula presented.) (E)=0 for every k ≥ 2.",

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T1 - Three kinds of numerical indices of a Banach space II

AU - Kim, Sung Guen

PY - 2016/3/31

Y1 - 2016/3/31

N2 - For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index (Formula presented.) (E), the symmetric multilinear numerical index (Formula presented.) (E) and the polynomial numerical index (Formula presented.) (E). First we show that (Formula presented.) (E**) ≤ (Formula presented.) (E) for I=m, s and present some inequalities among (Formula presented.) (E), (Formula presented.) (E) and (Formula presented.) (E). We also prove that if E is a strictly convex Banach space, then (Formula presented.) (E)=0 for every k ≥ 2.

AB - For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index (Formula presented.) (E), the symmetric multilinear numerical index (Formula presented.) (E) and the polynomial numerical index (Formula presented.) (E). First we show that (Formula presented.) (E**) ≤ (Formula presented.) (E) for I=m, s and present some inequalities among (Formula presented.) (E), (Formula presented.) (E) and (Formula presented.) (E). We also prove that if E is a strictly convex Banach space, then (Formula presented.) (E)=0 for every k ≥ 2.

KW - homogeneous polynomials

KW - multil̄inear mappings

KW - numerical index

KW - Numerical radius

KW - symmetric multilinear mappings

UR - https://www.scopus.com/pages/publications/84945218601

U2 - 10.2989/16073606.2015.1068236

DO - 10.2989/16073606.2015.1068236

M3 - Article

AN - SCOPUS:84945218601

SN - 1607-3606

VL - 39

SP - 153

EP - 166

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

IS - 2

ER -

Three kinds of numerical indices of a Banach space II

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