The polynomial numerical index of Lp(μ)

Sung Guen Kim

doi:10.5666/KMJ.2013.53.1.117

The polynomial numerical index of L_p(μ)

Sung Guen Kim

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

1 Scopus citations

Abstract

We show that for 1 < p < ∞, k,m ∈ N, n^(k)(l_p) = inf{n^(k)(l^m_p): m ∈ N} and that for any positive measure μ, n(^k)(L_p(μ)) ≥ n(^k)(l_p). We also prove that for every Q ∈ P(^kl_p: l_p) (1 < p < ∞), if _v(Q) = 0, then ||Q|| = 0.

Original language	English
Pages (from-to)	117-124
Number of pages	8
Journal	Kyungpook Mathematical Journal
Volume	53
Issue number	1
DOIs	https://doi.org/10.5666/KMJ.2013.53.1.117
State	Published - 2013

Keywords

Homogeneous polynomials
Polynomial numerical index

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10.5666/KMJ.2013.53.1.117

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title = "The polynomial numerical index of Lp(μ)",

abstract = "We show that for 1 < p < ∞, k,m ∈ N, n(k)(lp) = inf{n(k)(lmp): m ∈ N} and that for any positive measure μ, n(k)(Lp(μ)) ≥ n(k)(lp). We also prove that for every Q ∈ P(klp: lp) (1 < p < ∞), if v(Q) = 0, then ||Q|| = 0.",

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N2 - We show that for 1 < p < ∞, k,m ∈ N, n(k)(lp) = inf{n(k)(lmp): m ∈ N} and that for any positive measure μ, n(k)(Lp(μ)) ≥ n(k)(lp). We also prove that for every Q ∈ P(klp: lp) (1 < p < ∞), if v(Q) = 0, then ||Q|| = 0.

AB - We show that for 1 < p < ∞, k,m ∈ N, n(k)(lp) = inf{n(k)(lmp): m ∈ N} and that for any positive measure μ, n(k)(Lp(μ)) ≥ n(k)(lp). We also prove that for every Q ∈ P(klp: lp) (1 < p < ∞), if v(Q) = 0, then ||Q|| = 0.

KW - Homogeneous polynomials

KW - Polynomial numerical index

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DO - 10.5666/KMJ.2013.53.1.117

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SP - 117

EP - 124

JO - Kyungpook Mathematical Journal

JF - Kyungpook Mathematical Journal

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ER -

The polynomial numerical index of L_p(μ)

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