## Annals of Functional Analysis

### Operator approximate biprojectivity of locally compact quantum groups

#### Abstract

We initiate a study of operator approximate biprojectivity for quantum group algebra $L^{1}({\Bbb{G}})$, where $\mathbb{G}$ is a locally compact quantum group. We show that if $L^{1}({\Bbb{G}})$ is operator approximately biprojective, then $\mathbb{G}$ is compact. We prove that if $\mathbb{G}$ is a compact quantum group and $\mathbb{H}$ is a non-Kac-type compact quantum group such that both $L^{1}({\Bbb{G}})$ and $L^{1}({\Bbb{H}})$ are operator approximately biprojective, then $L^{1}({\Bbb{G}})\widehat{\otimes}L^{1}({\Bbb{H}})$ is operator approximately biprojective, but not operator biprojective.

#### Article information

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

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

https://projecteuclid.org/euclid.afa/1525420815

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

Mathematical Reviews number (MathSciNet)
MR3871911

Zentralblatt MATH identifier
07002088

#### 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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