Existence of universal members in certain families of bases of banach spaces

M. Zippin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Ina recent paper A. Pelczynski proved the existence of universal Schauder bases for several important families of bases.In the present paper some new existence problems are settled. For example, it is proved that the family of boundedly complete bases does not have a universal member.

Original languageEnglish
Pages (from-to)294-300
Number of pages7
JournalProceedings of the American Mathematical Society
Volume26
Issue number2
DOIs
StatePublished - 1970
Externally publishedYes

Keywords

  • Boundedly complete basis
  • Complementably universal basis
  • Complemented subbasis
  • Equivalent bases
  • Monotone basis
  • Norming function
  • Seminormalized basis
  • Shrinking basis
  • Subsequence homogeneous norming function
  • Unconditional basis
  • Universal basis

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