Unitary Banach algebras

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

doi:10.4064/sm162-1-3

Unitary Banach algebras

Julio Becerra Guerrero, Simon Cowell, Ángel Rodríguez Palacios, Geoffrey V. Wood

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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 l₁ 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.

Original language	English
Pages (from-to)	25-51
Number of pages	27
Journal	Studia Mathematica
Volume	162
Issue number	1
DOIs	https://doi.org/10.4064/sm162-1-3
Publication status	Published - 2004
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4064/sm162-1-3

Cite this

@article{c0716e0561e340789dd2b1cdd0e0f9af,

title = "Unitary Banach algebras",

abstract = "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 l1 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.",

author = "Guerrero, {Julio Becerra} and Simon Cowell and Palacios, {{\'A}ngel Rodr{\'i}guez} and Wood, {Geoffrey V.}",

year = "2004",

doi = "10.4064/sm162-1-3",

language = "English",

volume = "162",

pages = "25--51",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Instytut Matematyczny",

number = "1",

}

TY - JOUR

T1 - Unitary Banach algebras

AU - Guerrero, Julio Becerra

AU - Cowell, Simon

AU - Palacios, Ángel Rodríguez

AU - Wood, Geoffrey V.

PY - 2004

Y1 - 2004

N2 - 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 l1 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.

AB - 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 l1 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.

UR - http://www.scopus.com/inward/record.url?scp=2642540295&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2642540295&partnerID=8YFLogxK

U2 - 10.4064/sm162-1-3

DO - 10.4064/sm162-1-3

M3 - Article

AN - SCOPUS:2642540295

SN - 0039-3223

VL - 162

SP - 25

EP - 51

JO - Studia Mathematica

JF - Studia Mathematica

IS - 1

ER -

Unitary Banach algebras

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this