NA(L(n l1: l1))=NRA(L(n l1: l1))

Sung Guen Kim

doi:10.1007/s44146-022-00048-5

NA(L(ⁿ l₁: l₁))=NRA(L(ⁿ l₁: l₁))

Sung Guen Kim

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let n ≥ 2 and L(ⁿ E: E) denote the space of all continuous n-linear mappings from a Banach space E to itself. Let NA(L(ⁿ E: E)) denote the set of all norm attaining n-linear mappings in L(ⁿ E: E) and NRA(L(ⁿ E: E)) denote the set of all numerical radius attaining n-linear mappings in L(ⁿ E: E). In this paper we show that NA(L(ⁿ E: E))=NRA(L(ⁿ E: E)) if E = l₁. We also characterize NA(L(ⁿ l₁: l₁)).

Original language	English
Pages (from-to)	769-775
Number of pages	7
Journal	Acta Scientiarum Mathematicarum
Volume	88
Issue number	3-4
DOIs	https://doi.org/10.1007/s44146-022-00048-5
State	Published - Dec 2022

Keywords

norm attaining multilinear mappings
numerical radius attaining multilinear mappings

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10.1007/s44146-022-00048-5

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abstract = "Let n ≥ 2 and L(n E: E) denote the space of all continuous n-linear mappings from a Banach space E to itself. Let NA(L(n E: E)) denote the set of all norm attaining n-linear mappings in L(n E: E) and NRA(L(n E: E)) denote the set of all numerical radius attaining n-linear mappings in L(n E: E). In this paper we show that NA(L(n E: E))=NRA(L(n E: E)) if E = l1. We also characterize NA(L(n l1: l1)).",

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AU - Kim, Sung Guen

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N2 - Let n ≥ 2 and L(n E: E) denote the space of all continuous n-linear mappings from a Banach space E to itself. Let NA(L(n E: E)) denote the set of all norm attaining n-linear mappings in L(n E: E) and NRA(L(n E: E)) denote the set of all numerical radius attaining n-linear mappings in L(n E: E). In this paper we show that NA(L(n E: E))=NRA(L(n E: E)) if E = l1. We also characterize NA(L(n l1: l1)).

AB - Let n ≥ 2 and L(n E: E) denote the space of all continuous n-linear mappings from a Banach space E to itself. Let NA(L(n E: E)) denote the set of all norm attaining n-linear mappings in L(n E: E) and NRA(L(n E: E)) denote the set of all numerical radius attaining n-linear mappings in L(n E: E). In this paper we show that NA(L(n E: E))=NRA(L(n E: E)) if E = l1. We also characterize NA(L(n l1: l1)).

KW - norm attaining multilinear mappings

KW - numerical radius attaining multilinear mappings

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SP - 769

EP - 775

JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

IS - 3-4

ER -

NA(L(ⁿ l₁: l₁))=NRA(L(ⁿ l₁: l₁))

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