# REPRESENTATIONS OF LOCALLY COMPACT GROUPS ON QSLP-SPACES AND A P-ANALOG OF THE FOURIER-STIELTJES ALGEBRA

@article{Runde2004REPRESENTATIONSOL,
title={REPRESENTATIONS OF LOCALLY COMPACT GROUPS ON QSLP-SPACES AND A P-ANALOG OF THE FOURIER-STIELTJES ALGEBRA},
author={Volker Runde},
journal={Pacific Journal of Mathematics},
year={2004},
volume={221},
pages={379-397}
}
• V. Runde
• Published 3 February 2004
• Mathematics
• Pacific Journal of Mathematics
For a locally compact group G and p ∈ (1, oo), we define Bp(G) to be the space of all coefficient functions of isometric representations of G on quotients of subspaces of L p spaces. For p = 2, this is the usual Fourier-Stieltjes algebra. We show that Bp(G) is a commutative Banach algebra that contractively (isometrically, if G is amenable) contains the Figa-Talamanca-Herz algebra Ap(G). If 2 ≤ q ≤ p or p ≤ q ≤ 2, we have a contractive inclusion B q (G) ⊂ Bp(G). We also show that Bp(G) embeds…

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## References

SHOWING 1-10 OF 28 REFERENCES

### Amenable Locally Compact Groups

Collects the most recent results scattered throughout the literature on the theory of amenable groups, presenting a detailed investigation of the major features. The first part of the book discusses

### Arens Regularity of the Algebra of Operators on a Banach Space

A short proof is given that if E is a super‐reflexive Banach space, then B(E), the Banach algebra of operators on E with composition product, is Arens regular. Some remarks are made on necessary

• New York,
• 1984

### The ℒp spaces

• Mathematics
• 1969
The ℒp spaces which were introduced by A. Pełczyński and the first named author are studied. It is proved, e.g., that (i)X is an ℒp space if and only ifX* is and ℒq space (p−1+q−1=1). (ii) A

### Compactness of a Locally Compact Group G and Geometric Properties of Ap(G)

Abstract Let G be a locally compact topological group. A number of characterizations are given of the class of compact groups in terms of the geometric properties such as Radon-Nikodym property,

### Tensor products and p-induction of representations on Banach spaces

• Mathematics
• 2000
In this paper we obtain $L^p$ versions of the classical theorems of induced representations, namely, the inducing in stages theorem, the Kronecker product theorem, the Frobenius Reciprocity theorem