Polynomial numerical indices of Banach spaces with 1-unconditional bases

Han Ju Lee; Miguel Martín

doi:10.1016/j.laa.2011.05.043

Polynomial numerical indices of Banach spaces with 1-unconditional bases

Han Ju Lee
, Miguel Martín

Department of Mathematics Education

University of Granada

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

6 Scopus citations

Abstract

The only infinite-dimensional complex space with 1-unconditional basis which has polynomial numerical index of order 2 equal to 1 is c ₀. In the real case, there is no space of this type. We also show that, in the complex case, if X is an infinite-dimensional Banach sequence space with absolute norm whose Köthe dual is norming and has polynomial numerical index of order 2 equal to 1, then c ₀⊂X⊂ℓ _∞. In the real case, again there is no space of this type.

Original language	English
Pages (from-to)	2001-2008
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	437
Issue number	8
DOIs	https://doi.org/10.1016/j.laa.2011.05.043
State	Published - 15 Oct 2012

Keywords

Absolute norm
Köthe space
Numerical index
Polynomial
Unconditional basis

Access to Document

10.1016/j.laa.2011.05.043

Cite this

@article{9499a7bb55f844eb93bfa9396e4a3f46,

title = "Polynomial numerical indices of Banach spaces with 1-unconditional bases",

abstract = "The only infinite-dimensional complex space with 1-unconditional basis which has polynomial numerical index of order 2 equal to 1 is c 0. In the real case, there is no space of this type. We also show that, in the complex case, if X is an infinite-dimensional Banach sequence space with absolute norm whose K{\"o}the dual is norming and has polynomial numerical index of order 2 equal to 1, then c 0⊂X⊂ℓ ∞. In the real case, again there is no space of this type.",

keywords = "Absolute norm, K{\"o}the space, Numerical index, Polynomial, Unconditional basis",

author = "Lee, \{Han Ju\} and Miguel Mart{\'i}n",

year = "2012",

month = oct,

day = "15",

doi = "10.1016/j.laa.2011.05.043",

language = "English",

volume = "437",

pages = "2001--2008",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "8",

}

TY - JOUR

T1 - Polynomial numerical indices of Banach spaces with 1-unconditional bases

AU - Lee, Han Ju

AU - Martín, Miguel

PY - 2012/10/15

Y1 - 2012/10/15

N2 - The only infinite-dimensional complex space with 1-unconditional basis which has polynomial numerical index of order 2 equal to 1 is c 0. In the real case, there is no space of this type. We also show that, in the complex case, if X is an infinite-dimensional Banach sequence space with absolute norm whose Köthe dual is norming and has polynomial numerical index of order 2 equal to 1, then c 0⊂X⊂ℓ ∞. In the real case, again there is no space of this type.

AB - The only infinite-dimensional complex space with 1-unconditional basis which has polynomial numerical index of order 2 equal to 1 is c 0. In the real case, there is no space of this type. We also show that, in the complex case, if X is an infinite-dimensional Banach sequence space with absolute norm whose Köthe dual is norming and has polynomial numerical index of order 2 equal to 1, then c 0⊂X⊂ℓ ∞. In the real case, again there is no space of this type.

KW - Absolute norm

KW - Köthe space

KW - Numerical index

KW - Polynomial

KW - Unconditional basis

UR - https://www.scopus.com/pages/publications/84864430032

U2 - 10.1016/j.laa.2011.05.043

DO - 10.1016/j.laa.2011.05.043

M3 - Article

AN - SCOPUS:84864430032

SN - 0024-3795

VL - 437

SP - 2001

EP - 2008

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 8

ER -

Polynomial numerical indices of Banach spaces with 1-unconditional bases

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this