Premium
Examples of Factorization Without Bounded Approximate Units
Author(s) -
Willis George
Publication year - 1992
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-64.3.602
Subject(s) - mathematics , bounded function , separable space , connection (principal bundle) , commutative property , factorization , element (criminal law) , banach algebra , product (mathematics) , algebra over a field , banach space , pure mathematics , discrete mathematics , mathematical analysis , algorithm , geometry , political science , law
Examples are given of Banach algebras which do not have bounded approximate units but in which every element is a product. Another algebra is constructed in which there are elements which are not products but every element is the sum of two products. Most of the examples are commutative and separable. These examples suggest that there may be a connection between factorization questions and the topology of the carrier space of a Banach algebra.