The compactum and finite dimensionality in Banach algebras
Given a Banach algebra A, the compactum of A is defined to be the set of elements x∈A such that the operator a→xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1982-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000246 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Given a Banach algebra A, the compactum of A is defined to be the set of elements x∈A such that the operator a→xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in terms of the compactum and the socle of A. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |