Automatic Continuity and a Problem of Kaplansky.
Abstract
Automatic continuity is the study of restrictions that can be imposed upon the domain and/or range of an operator that will guarantee the continuity of the operator. Theorems of this nature are interesting by themselves, but they sometimes have surprising applications as well - the use of a continuity theorem in Johnson's proof that all complete algebra norms in a semisimple Banach algebra are equivalent being just one example. The purpose of this dissertation is to provide an introduction to the subject of automatic continuity, with emphasis on this problem of Kaplansky, the work of Bade and Curtis, and a discussion of Dales' construction.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1977
- Accession Number
- ADA061786
Entities
People
- John A. Ausink
Organizations
- Air Force Institute of Technology