Representations of locally compact groups on QSL_p-spaces and a p-analog of the Fourier-Stieltjes algebra
| dc.creator | Runde, Volker | |
| dc.date | 2004-02-03 | |
| dc.date | 2004-10-20 | |
| dc.date.accessioned | 2026-07-07T06:22:01Z | |
| dc.date.available | 2026-07-07T06:22:01Z | |
| dc.description | For a locally compact group $G$ and $p \in (1,\infty)$, we define $B_p(G)$ 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 $B_p(G)$ is a commutative Banach algebra that contractively (isometrically, if $G$ is amenable) contains the Figà-Talamanca--Herz algebra $A_p(G)$. If $2 \leq q \leq p$ or $p \leq q \leq 2$, we have a contractive inclusion $B_q(G) \subset B_p(G)$. We also show that $B_p(G)$ embeds contractively into the multiplier algebra of $A_p(G)$ and is a dual space. For amenable $G$, this multiplier algebra and $B_p(G)$ are isometrically isomorphic. | |
| dc.description | 19 pages; LaTeX2e; two references added | |
| dc.identifier | https://arxiv.org/abs/math/0402018 | |
| dc.identifier | http://arxiv.org/abs/math/0402018 | |
| dc.identifier | Pacific J. Math. 221 (2005), 379-397 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95787 | |
| dc.subject | Functional Analysis | |
| dc.subject | Representation Theory | |
| dc.subject | Primary 46J99; Secondary 22D12, 22D35, 43A07, 43A15, 43A65, 46J99 | |
| dc.title | Representations of locally compact groups on QSL_p-spaces and a p-analog of the Fourier-Stieltjes algebra | |
| dc.type | text |