Abstract
In this paper one of the possible p-operator space structures of the p-analog of the Fourier-Stieltjes algebra will be introduced, and to some extend will be studied. This special sort of p-operator structure will be given from the predual of this Fourier type algebra, that is the algebra of universal p-pseudofunctions. Furthermore, some applicable and expected results will be proven. Current paper can be considered as a new gate into the collection of problems around the p-analog of the Fourier-Stieltjes algebra, in the p-operator space structure point of view.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amini, M., Medghalchi, A.R.: Restricted algebras on inverse semigroups I, representation theory. Math. Nachr. 279(16), 1739–1748 (2006)
Dales, H. G., Polyakov, M. E.: Multi-normed spaces, ArXiv: 1112.15148v2
Daws, M.: \(p\)-Operator spaces and Figà-Talamanca-Herz algebras. J. Operator Theory 63(1), 47–83 (2010)
De Cannière, J., Enock, M., Schwartz, J.-M.: Sur deux résultats d’analyse harmonique non-commutative: Une application de la théorie des algèbres de Kac. J. Operator Theory 5, 171–194 (1981)
Effros, E.G., Ruan, Z.-J.: A new approach to operator spaces. Canad. J. Math. 34, 329–337 (1991)
Effros, E.G., Ruan, Z.-J.: Operator Spaces, London Math. Soc. Monogr. (N.S.) 23 Clarendon Press, Oxford University Press, New York, (2000)
Eymard, P.: L’algébre de Fourier d’un groupe localement compact. Bull. Soc. Math. France 92, 181–236 (1964)
Figà-Talamanca, A.: Translation invariant operators in \(L_p\). Duke Math. J. 32, 495–501 (1965)
Folland, G.B.: A course in abstract harmonic analysis. CRC PRESS, Florida (1995)
Gardella, E.: A modern look at algebras of operators on \(L_p\)-spaces, ArXiv:1909.12096v1
Herz, C.: Une généralisation de la notion de transformée de Fourier-Stieltjes. Ann. Inst. Fourier 24, 145–157 (1974)
Herz, C.: The theory of \(p\)-spaces with an application to convolution operators, its second dual. Trans. Amer. Math. Soc. 154, 69–82 (1971)
Ilie, M.: A note on \(p\)-completely bounded homomorphisms of the Figà-Talamanca-Herz algebras. J. Math. Anal. Appl. 419, 273–284 (2014)
Ilie, M., Spronk, N.: Completely bounded homomorphisms of the Fourier algebra. J. Funct. Anal. 225, 480–499 (2005)
Losert, V.: Properties of the Fourier algebra that are equivalent to amenability. Proc. Amer. Math. Soc. 92, 347–354 (1984)
Le Merdy, C.: Factorization of \(p\)-completely bounded multilinear maps. Pacic J. Math. 172, 187–213 (1996)
Paterson, A.L.T.: The Fourier algebra for locally compact groupoids. Canad. J. Math. 56, 1259–1289 (2004)
Pisier, G.: Similarity problems and completely bounded maps, second, expanded edition. Lecture Notes in Math, vol. 1618. Springer-Verlag, Berlin (2001)
Runde, V.: Representations of locally compact groups on \({QSL}_p\)-spaces and a \(p\)-analog of the Fourier-Stieltjes algebra. Pacific J. Math. 221(2), 379–397 (2005)
Yousefi, M.Shams: \(p\)-analog of the semigroup Fourier-Stieltjes algebras. Iranian J. Math. Sci. and Inf. 10(2), 55–66 (2015)
Acknowledgements
We would like to thank Eusebio Gardella for his great hints and providing some of his unpublished papers for us.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ahmadpoor, M.A., Yousefi, M.S. A note on the p-operator space structure of the p-analog of the Fourier-Stieltjes algebra. Rend. Circ. Mat. Palermo, II. Ser 71, 153–170 (2022). https://doi.org/10.1007/s12215-021-00601-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-021-00601-1
Keywords
- p-operator spaces
- p-analog of the Fourier-Stieltjes algebras
- \(QSL_p\)-spaces
- Universal representation