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 hdl:20.500.11880/26285 http://dx.doi.org/10.22028/D291-26229 |
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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