The Daugavet property of C*-algebras and non-commutative L p-spaces

Timur Oikhberg

doi:10.1023/A:1012023526639

The Daugavet property of C*-algebras and non-commutative L _p-spaces

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

Abstract

We prove that a C*-algebra A or a predual N* of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative L_p-spaces corresponding to non-atomic von Neumann algebras.

Original language	English (US)
Pages (from-to)	59-73
Number of pages	15
Journal	Positivity
Volume	6
Issue number	1
DOIs	https://doi.org/10.1023/A:1012023526639
State	Published - 2002
Externally published	Yes

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
General Mathematics

Online availability

10.1023/A:1012023526639

Library availability

Discover UIUC Full Text

Cite this

@article{88376e2f3c8d492888905b0b4d53413c,

title = "The Daugavet property of C*-algebras and non-commutative L p-spaces",

abstract = "We prove that a C*-algebra A or a predual N* of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative Lp-spaces corresponding to non-atomic von Neumann algebras.",

author = "Timur Oikhberg",

note = "The author was supported by the NSF grant DMS-9970369.",

year = "2002",

doi = "10.1023/A:1012023526639",

language = "English (US)",

volume = "6",

pages = "59--73",

journal = "Positivity",

issn = "1385-1292",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - The Daugavet property of C*-algebras and non-commutative L p-spaces

AU - Oikhberg, Timur

N1 - The author was supported by the NSF grant DMS-9970369.

PY - 2002

Y1 - 2002

N2 - We prove that a C*-algebra A or a predual N* of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative Lp-spaces corresponding to non-atomic von Neumann algebras.

AB - We prove that a C*-algebra A or a predual N* of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative Lp-spaces corresponding to non-atomic von Neumann algebras.

UR - http://www.scopus.com/inward/record.url?scp=0141454945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141454945&partnerID=8YFLogxK

U2 - 10.1023/A:1012023526639

DO - 10.1023/A:1012023526639

M3 - Article

AN - SCOPUS:0141454945

SN - 1385-1292

VL - 6

SP - 59

EP - 73

JO - Positivity

JF - Positivity

IS - 1

ER -