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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-44134
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4413/


Operator space structure and amenability for Figa-Talamanca-Herz algebras

Lambert, Anselm ; Neufang, Matthias ; Runde, Volker

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Freie Schlagwörter (Englisch): operator sequence spaces , locally compact groups
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universit├Ąt des Saarlandes
Bandnummer: 78
Sprache: Englisch
Erstellungsjahr: 2003
Publikationsdatum: 02.12.2011
Kurzfassung auf Englisch: 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.
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