## Tsukuba Journal of Mathematics

### Generalized Fourier-Stieltjes algebra

G. A. Bagheri-Bardi

#### 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

https://projecteuclid.org/euclid.tkbjm/1438951815

Digital Object Identifier
doi:10.21099/tkbjm/1438951815

Mathematical Reviews number (MathSciNet)
MR3383876

Zentralblatt MATH identifier
1329.43001

#### 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