Tsukuba Journal of Mathematics

Generalized Fourier-Stieltjes algebra

G. A. Bagheri-Bardi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let $\{G_{}\}^n_{i=1}$ be locally compact groups and $\mathscr{H}$ be Hilbert space. We define the n-variable Fourier-Stieltjes algebra $B(\Pi^{n}_{1} G_{i}, \mathrm{B}(\mathscr{H}))$ consists all functions \[ \phi : G_{1} \times \cdot \times G_{n} \rightarrow \mathrm{B}(\mathscr{H}) \] for which there exists unitary representations $\pi_{i} : \mathbb{G}_{i} \rightarrow \mathrm{B}(\mathscr{H}_i)$ and a diagram of bounded operators \[ \mathscr{H} \rightarrow^{V} \mathscr{H}_n \rightarrow^{T_{n-1}} \mathscr{H}_{n-1} \rightarrow^{T_{1}} \mathscr{H_1} \rightarrow^{U} \mathscr{H} \] with \[ \phi(s_{1},..., s_{n}) = U\pi_{1}(s_1)T_{1}\pi_{2})s_{2}) \cdot \pi_{n-1}(s_{n-1})T_{n}\pi_{n}(s_{n}V \] We extend the pointwise product on $B(\Pi^{n}_{1} G_{i}, \mathrm{B}(\mathscr{H}))$ under which it forms a completely contractive commutative unital Banach algebra. A diagram of its subalgebras will be introduced.

Article information

Source
Tsukuba J. Math., Volume 39, Number 1 (2015), 15-28.

Dates
First available in Project Euclid: 7 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1438951815

Digital Object Identifier
doi:10.21099/tkbjm/1438951815

Mathematical Reviews number (MathSciNet)
MR3383876

Zentralblatt MATH identifier
1329.43001

Subjects
Primary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 47L25: Operator spaces (= matricially normed spaces) [See also 46L07] 46L07: Operator spaces and completely bounded maps [See also 47L25]

Keywords
Fourier-Stiltjes algebras Operator spaces Operator spaces and completely bounded maps

Citation

Bagheri-Bardi, G. A. Generalized Fourier-Stieltjes algebra. Tsukuba J. Math. 39 (2015), no. 1, 15--28. doi:10.21099/tkbjm/1438951815. https://projecteuclid.org/euclid.tkbjm/1438951815


Export citation