caa a22 4500 445868767 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00605-010-0250-8 doi (NATIONALLICENCE)springer-10.1007/s00605-010-0250-8 Mortini Raymond Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine, Ile du Saulcy, 57045, Metz, France aut Generalized stable ranks for commutative Banach algebras [Elektronische Daten] [Raymond Mortini] We introduce the notion of generalized E-stable ranks for commutative unital Banach algebras and determine these ranks for the disk-algebra $${A(\mathbb{D})}$$, many of its subalgebras, and the algebra H ∞ of bounded holomorphic functions in the unit disk. Relations to L-sets and separating algebras, notions due to Csordas and Reiter, are given, too. Finally we show that the absolute stable rank of $${A(\mathbb{D})}$$ and H ∞ is bigger than 2. Springer-Verlag, 2010 Commutative Banach algebras nationallicence Stable ranks nationallicence Disk-algebra nationallicence Bounded analytic functions nationallicence Separating algebras nationallicence Bézout equation nationallicence Monatshefte für Mathematik Springer Vienna 164/3(2011-11-01), 299-311 0026-9255 164:3<299 2011 164 605 https://doi.org/10.1007/s00605-010-0250-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0250-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mortini Raymond Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine, Ile du Saulcy, 57045, Metz, France aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/3(2011-11-01), 299-311 0026-9255 164:3<299 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer