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.

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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

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Algebra
  • Analytic Functions
  • Automatic
  • Banach Space
  • Complex Numbers
  • Construction
  • Continuity
  • Functional Analysis
  • Identities
  • Linear Algebra
  • Mathematics
  • Numbers
  • Real Numbers
  • Sequences
  • Topology

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Military History
  • Systems Analysis and Design