Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter December 19, 2018

Multi-norm structure based on enveloping š¶āˆ—-algebras

  • Marzieh Shams Yousefi EMAIL logo

Abstract

A non-trivial multi-norm structure based on the enveloping C*-algebras will be discussed in this paper. The main example is group C*-algebras on compact groups. Also a (generalizing) non-trivial multi-norm structure based on the Fourier and Fourierā€“Stieltjes algebras on compact groups will be given.

MSC 2010: 47L10; 46L45

Acknowledgements

The author is indebted to the anonymous referee for critical suggestions, especially Remark 2.13, which improved the paper.

References

[1] H. G. Dales, Multiā€“norms, Acta Comment. Univ. Tartu. Math. 18 (2014), no. 1, 159ā€“184. 10.12697/ACUTM.2014.18.15Search in Google Scholar

[2] H. G. Dales, M. Daws, H. L. Pham and P. Ramsden, Multi-norms and the injectivity of Lpā¢(G), J. Lond. Math. Soc. (2) 86 (2012), 779ā€“809. 10.1112/jlms/jds026Search in Google Scholar

[3] H. G. Dales and M. Polyakov, Multi-normed spaces, Dissertationes Math. (Rozprawy Mat.) 488 (2012), 1ā€“165. 10.4064/dm488-0-1Search in Google Scholar

[4] P. Eymard, Lā€™algĆØbre de Fourier dā€™un groupe localment compact, Bull. Soc. Math. France 92 (1964), 181ā€“236. 10.24033/bsmf.1607Search in Google Scholar

[5] J. B. Foland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995. Search in Google Scholar

[6] P. Harmand, D. Werner and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993. 10.1007/BFb0084355Search in Google Scholar

[7] P. Ramsden, Homological properties of semigroup algebras, Ph.D. thesis, Leeds University, 2009. 10.1007/s00233-009-9169-6Search in Google Scholar

[8] D. P. Williams, Crossed Products of C*-algebras, Math. Surveys Monogr. 134, American Mathematical Society, Providence, 2007. 10.1090/surv/134Search in Google Scholar

Received: 2018-09-10
Revised: 2018-11-26
Accepted: 2018-12-04
Published Online: 2018-12-19
Published in Print: 2019-10-01

Ā© 2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 25.4.2024 from https://www.degruyter.com/document/doi/10.1515/apam-2018-0150/html
Scroll to top button