Bounded Generators of Linear Spaces,

Abstract

Let S sub phi = (x epsilon X: (sup sub alpha) (phi sub alpha) (x) < infinity where phi = (phi sub alpha) is a family of semi-norms determining the topology of X. It is shown that phi may be chosen so S sub phi is dense if X has a bounded generating set if there is a continuous norm on X star. It is shown that these conditions hold for separable Frechet spaces and for quotients of products of Banach spaces. An example is given of a Frechet space containing no bounded generating set thus contradicting an assertion of L. Mate that S sub phi is dense for Frechet spaces. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1971
Accession Number
AD0727277

Entities

People

  • T. Ito
  • T. Seidman

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Cooperation
  • Families (Human)
  • Generators
  • Mathematics
  • Topology

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space