WEAK CONVERGENCE IN CERTAIN SPECIAL BANACH SPACES,

Abstract

This report gives a theorem which provides a set of necessary and sufficient conditions to ensure the weak compactness of a set in the space of Bochner-integrable functions on a finite measure space taking values in a reflexive Banach space. The conditions and the proof are analogous to those in the scalar-valued case. Three other theorems and their proofs give preparatory material including a description of linear functionals on the space mentioned above and its weak completeness. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1963
Accession Number
AD0433476

Entities

People

  • S. D. Chatterji

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Convergence
  • Materials
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space