Interpolation of Schur multiplier spaces

Quanhua Xu

doi:10.1007/PL00004817

Interpolation of Schur multiplier spaces

Quanhua Xu^*

^*Corresponding author for this work

UMR de Mathématiques

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

3 Scopus citations

Abstract

Let M(S_p) denote the space of all Schur mulptiliers on the Schatten class S_p. It is proved that there is a linear map which is a contraction on both M(S₂) and M(S_∞) but which is not bounded on M(S_p) for all 2 < p < ∞. Consequently, for any 2 < p < ∞, M(S_p) is not an interpolation space between M(S₂) and M(S_∞).

Original language	English
Pages (from-to)	707-715
Number of pages	9
Journal	Mathematische Zeitschrift
Volume	235
Issue number	4
DOIs	https://doi.org/10.1007/PL00004817
State	Published - Dec 2000
Externally published	Yes

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10.1007/PL00004817

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@article{f38907713ab449b298166ee517f33392,

title = "Interpolation of Schur multiplier spaces",

abstract = "Let M(Sp) denote the space of all Schur mulptiliers on the Schatten class Sp. It is proved that there is a linear map which is a contraction on both M(S2) and M(S∞) but which is not bounded on M(Sp) for all 2 < p < ∞. Consequently, for any 2 < p < ∞, M(Sp) is not an interpolation space between M(S2) and M(S∞).",

author = "Quanhua Xu",

year = "2000",

month = dec,

doi = "10.1007/PL00004817",

language = "英语",

volume = "235",

pages = "707--715",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "4",

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TY - JOUR

T1 - Interpolation of Schur multiplier spaces

AU - Xu, Quanhua

PY - 2000/12

Y1 - 2000/12

N2 - Let M(Sp) denote the space of all Schur mulptiliers on the Schatten class Sp. It is proved that there is a linear map which is a contraction on both M(S2) and M(S∞) but which is not bounded on M(Sp) for all 2 < p < ∞. Consequently, for any 2 < p < ∞, M(Sp) is not an interpolation space between M(S2) and M(S∞).

AB - Let M(Sp) denote the space of all Schur mulptiliers on the Schatten class Sp. It is proved that there is a linear map which is a contraction on both M(S2) and M(S∞) but which is not bounded on M(Sp) for all 2 < p < ∞. Consequently, for any 2 < p < ∞, M(Sp) is not an interpolation space between M(S2) and M(S∞).

UR - https://www.scopus.com/pages/publications/0034365231

U2 - 10.1007/PL00004817

DO - 10.1007/PL00004817

M3 - 文章

AN - SCOPUS:0034365231

SN - 0025-5874

VL - 235

SP - 707

EP - 715

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 4

ER -

Interpolation of Schur multiplier spaces

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