Please use this identifier to cite or link to this item: doi:10.22028/D291-26229
Title: Operator space structure and amenability for Figa-Talamanca-Herz algebras
Author(s): Lambert, Anselm
Neufang, Matthias
Runde, Volker
Language: English
Year of Publication: 2003
Free key words: operator sequence spaces
locally compact groups
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: Column and row operator spaces - which we denote by COL and ROW, respectively - over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group G and p,p\text{'}\in(1,\infty) with \frac{1}{p}+\frac{1}{p\text{'}}=1, we use the operator space structure on CB(COL(L^{p\text{'}}(G))) to equip the Figa-Talamanca-Herz algebra A_{p}(G) with an operator space structure, turning it into a quantized Banach algebra. Moreover, we show that, for p\leq q\leq 2 or 2\leq q\leq p and amenable G, the canonical inclusion A_{q}(G)\subset A_{p}(G) is completely bounded (with cb-norm at most K_{\mathbb{G}}^{2}, where K_{\mathbb{G}} is Grothendieck's constant). As an application, we show that G is amenable if and only if A_{p}(G) is operator amenable for all - and equivalently for one - p\in(1,\infty); this extends a theorem by Z.-J. Ruan.
Link to this record: urn:nbn:de:bsz:291-scidok-44134
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 78
Date of registration: 2-Dec-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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