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

Access to Document

10.5666/KMJ.2013.53.1.117

Cite this

@article{051170a2419e436693e61f73dce425b5,

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.",

keywords = "Homogeneous polynomials, Polynomial numerical index",

author = "Kim, \{Sung Guen\}",

year = "2013",

doi = "10.5666/KMJ.2013.53.1.117",

language = "English",

volume = "53",

pages = "117--124",

journal = "Kyungpook Mathematical Journal",

issn = "1225-6951",

publisher = "Kyungmoon Publishing",

number = "1",

}

TY - JOUR

T1 - The polynomial numerical index of Lp(μ)

AU - Kim, Sung Guen

PY - 2013

Y1 - 2013

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

UR - https://www.scopus.com/pages/publications/84884162466

U2 - 10.5666/KMJ.2013.53.1.117

DO - 10.5666/KMJ.2013.53.1.117

M3 - Article

AN - SCOPUS:84884162466

SN - 1225-6951

VL - 53

SP - 117

EP - 124

JO - Kyungpook Mathematical Journal

JF - Kyungpook Mathematical Journal

IS - 1

ER -

The polynomial numerical index of L_p(μ)

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this