SOME CLASS OF NUMERICAL RADIUS PEAK n-LINEAR MAPPINGS ON lp-SPACES

S. G. Kim

doi:10.30970/ms.57.1.10-15

SOME CLASS OF NUMERICAL RADIUS PEAK n-LINEAR MAPPINGS ON lp-SPACES

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

Abstract

For n≥ 2 and a real Banach space E, £(^ⁿE: E) denotes the space of all continuous n-linear mappings from E to itself. Let (Formula presented) For T€ £(^ⁿE: E), we define (Formula presented) where v(T) denotes the numerical radius of T. T is called numerical radius peak mapping if there is [x*, (x_₁,…, x_{_n})]€ Π(E) such that Nr(T) = {±[x*, (x_₁,…, x_{_n})]}. In this paper, we investigate some class of numerical radius peak mappings in L(^ⁿl_{_p}: l_{_p}) for 1<p <∞. Let (a_{_j})_{_j€ℕ} be a bounded sequence in ℝ such that sup_{_j€ℕ} | aj| > 0. Defne T€ £(^ⁿl_{_p}: l_{_p}) by (Formula presented) In particular is proved the following statements: 1. If 1<p <+∞ then T is a numerical radius peak mapping if and only if there is j_{_o}€ ℕ such that (Formula presented) 2. If p = 1 then T is not a numerical radius peak mapping in £(^ⁿ l: l).

Original language	English
Pages (from-to)	10-15
Number of pages	6
Journal	Matematychni Studii
Volume	57
Issue number	1
DOIs	https://doi.org/10.30970/ms.57.1.10-15
State	Published - 2022

Keywords

numerical radius peak mappings
numerical radius points

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10.30970/ms.57.1.10-15

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title = "SOME CLASS OF NUMERICAL RADIUS PEAK n-LINEAR MAPPINGS ON lp-SPACES",

abstract = "For n≥ 2 and a real Banach space E, £(nE: E) denotes the space of all continuous n-linear mappings from E to itself. Let (Formula presented) For T€ £(nE: E), we define (Formula presented) where v(T) denotes the numerical radius of T. T is called numerical radius peak mapping if there is [x*, (x1,…, xn)]€ Π(E) such that Nr(T) = {±[x*, (x1,…, xn)]}. In this paper, we investigate some class of numerical radius peak mappings in L(nlp: lp) for 1j)j€ℕ be a bounded sequence in ℝ such that supj€ℕ | aj| > 0. Defne T€ £(nlp: lp) by (Formula presented) In particular is proved the following statements: 1. If 1o€ ℕ such that (Formula presented) 2. If p = 1 then T is not a numerical radius peak mapping in £(n l: l).",

keywords = "numerical radius peak mappings, numerical radius points",

author = "Kim, {S. G.}",

note = "Publisher Copyright: {\textcopyright} S. G. Kim, 2022",

year = "2022",

doi = "10.30970/ms.57.1.10-15",

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AU - Kim, S. G.

N1 - Publisher Copyright: © S. G. Kim, 2022

PY - 2022

Y1 - 2022

N2 - For n≥ 2 and a real Banach space E, £(nE: E) denotes the space of all continuous n-linear mappings from E to itself. Let (Formula presented) For T€ £(nE: E), we define (Formula presented) where v(T) denotes the numerical radius of T. T is called numerical radius peak mapping if there is [x*, (x1,…, xn)]€ Π(E) such that Nr(T) = {±[x*, (x1,…, xn)]}. In this paper, we investigate some class of numerical radius peak mappings in L(nlp: lp) for 1j)j€ℕ be a bounded sequence in ℝ such that supj€ℕ | aj| > 0. Defne T€ £(nlp: lp) by (Formula presented) In particular is proved the following statements: 1. If 1o€ ℕ such that (Formula presented) 2. If p = 1 then T is not a numerical radius peak mapping in £(n l: l).

AB - For n≥ 2 and a real Banach space E, £(nE: E) denotes the space of all continuous n-linear mappings from E to itself. Let (Formula presented) For T€ £(nE: E), we define (Formula presented) where v(T) denotes the numerical radius of T. T is called numerical radius peak mapping if there is [x*, (x1,…, xn)]€ Π(E) such that Nr(T) = {±[x*, (x1,…, xn)]}. In this paper, we investigate some class of numerical radius peak mappings in L(nlp: lp) for 1j)j€ℕ be a bounded sequence in ℝ such that supj€ℕ | aj| > 0. Defne T€ £(nlp: lp) by (Formula presented) In particular is proved the following statements: 1. If 1o€ ℕ such that (Formula presented) 2. If p = 1 then T is not a numerical radius peak mapping in £(n l: l).

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KW - numerical radius points

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SOME CLASS OF NUMERICAL RADIUS PEAK n-LINEAR MAPPINGS ON lp-SPACES

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