Geodesic
Unitary Banach algebras
Julio Becerra Guerrero 1   ; Simon Cowell 2   ; Ángel Rodríguez Palacios 3   ; Geoffrey V. Wood 2
1 Departamento de Matemática Aplicada Facultad de Ciencias Universidad de Granada 18071-Granada, Spain
2 Department of Mathematics University of Wales Swansea Swansea SA2 8PP, Wales, UK
3 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071-Granada, Spain
Studia Mathematica, Tome 162 (2004) no. 1, pp. 25-51 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the $C^*$-algebras and the $\ell _1$ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of $C^*$-algebras are given.
DOI : 10.4064/sm162-1-3
Keywords: banach algebra invertible element which has norm whose inverse has norm called unitary algebra unitary closed convex hull unitary elements closed unit ball main examples * algebras ell group algebra group paper different characterizations unitary algebras obtained terms numerical ranges dentability holomorphy process characterizations * algebras given

Julio Becerra Guerrero  1   ; Simon Cowell  2   ; Ángel Rodríguez Palacios  3   ; Geoffrey V. Wood  2

1 Departamento de Matemática Aplicada Facultad de Ciencias Universidad de Granada 18071-Granada, Spain
2 Department of Mathematics University of Wales Swansea Swansea SA2 8PP, Wales, UK
3 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071-Granada, Spain 
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Julio Becerra Guerrero; Simon Cowell; Ángel Rodríguez Palacios; Geoffrey V. Wood. Unitary Banach algebras. Studia Mathematica, Tome 162 (2004) no. 1, pp. 25-51. doi: 10.4064/sm162-1-3

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