INVARIANT SUBSPACES OF COMPLETELY CONTINOUS OPERATIONS

Abstract

A proof is presented of the theorem that if B is a Banach space and if T is a completely continuous operator in B, there then exist proper invariant subspaces of T. The proof assumes strong convergence, complete continuity in the sense that any bounded set is transformed by T into a set with compact closure, and a strictly convex norm. The same theorem is proved for a Hilbert space; the theorem utilizes the concepts of weak and strong convergenece of elements and operators. The simplifying feature of the latter proof is that the metric propjections coincide with the usual orthogonal projections.

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Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1953
Accession Number
AD0012105

Entities

People

  • K.t. Smith
  • N. Aronszajn

Organizations

  • University of Kansas

Tags

DTIC Thesaurus Topics

  • Approximation (Mathematics)
  • Banach Space
  • Continuity
  • Contracts
  • Convergence
  • Extrapolation
  • Hilbert Space
  • Integrals
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • New York
  • Sequences
  • Topology

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space