Advances in Operator Theory

Uniformly bounded representations and completely bounded multipliers of $\mathrm {SL}(2,\mathbb{R})$

Francesca Astengo, Michael G. Cowling, and Bianca Di Blasio

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Abstract

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of $\mathrm {SL}(2,\mathbb{R})$ as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal.

Article information

Source
Adv. Oper. Theory, Volume 3, Number 1 (2018), 247-270.

Dates
Received: 24 July 2017
Accepted: 17 August 2017
First available in Project Euclid: 5 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512497961

Digital Object Identifier
doi:10.22034/aot.1707-1207

Mathematical Reviews number (MathSciNet)
MR3730348

Zentralblatt MATH identifier
06804325

Subjects
Primary: 43A80: Analysis on other specific Lie groups [See also 22Exx]
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]

Keywords
completely bounded multipliers Fourier algebra $\mathrm {SL}(2,\mathbb{R})$

Citation

Astengo, Francesca; Cowling, Michael G.; Di Blasio, Bianca. Uniformly bounded representations and completely bounded multipliers of $\mathrm {SL}(2,\mathbb{R})$. Adv. Oper. Theory 3 (2018), no. 1, 247--270. doi:10.22034/aot.1707-1207. https://projecteuclid.org/euclid.aot/1512497961


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References

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