Annals of Functional Analysis

Operator approximate biprojectivity of locally compact quantum groups

Mohammad Reza Ghanei and Mehdi Nemati

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Abstract

We initiate a study of operator approximate biprojectivity for quantum group algebra L1(G), where G is a locally compact quantum group. We show that if L1(G) is operator approximately biprojective, then G is compact. We prove that if G is a compact quantum group and H is a non-Kac-type compact quantum group such that both L1(G) and L1(H) are operator approximately biprojective, then L1(G)ˆL1(H) is operator approximately biprojective, but not operator biprojective.

Article information

Source
Ann. Funct. Anal., Volume 9, Number 4 (2018), 514-524.

Dates
Received: 17 June 2017
Accepted: 20 November 2017
First available in Project Euclid: 4 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.afa/1525420815

Digital Object Identifier
doi:10.1215/20088752-2017-0065

Mathematical Reviews number (MathSciNet)
MR3871911

Zentralblatt MATH identifier
07002088

Subjects
Primary: 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22]
Secondary: 46M10: Projective and injective objects [See also 46A22] 46L07: Operator spaces and completely bounded maps [See also 47L25]

Keywords
locally compact quantum group operator approximate biprojectivity tensor product of compact quantum groups

Citation

Ghanei, Mohammad Reza; Nemati, Mehdi. Operator approximate biprojectivity of locally compact quantum groups. Ann. Funct. Anal. 9 (2018), no. 4, 514--524. doi:10.1215/20088752-2017-0065. https://projecteuclid.org/euclid.afa/1525420815


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