On Perfectly Homogeneous Bases in Quasi-Banach Spaces View Full Text


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Article Info

DATE

2009

AUTHORS

F. Albiac, C. Leránoz

ABSTRACT

For 0 < p < ∞ the unit vector basis of ℓ p has the property of perfect homogeneity: it is equivalent to all its normalized block basic sequences, that is, perfectly homogeneous bases are a special case of symmetric bases. For Banach spaces, a classical result of Zippin (1966) proved that perfectly homogeneous bases are equivalent to either the canonical c 0 -basis or the canonical ℓ p -basis for some 1 ≤ p < ∞ . In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases of ℓ p for 0 < p < 1 as well amongst bases in nonlocally convex quasi-Banach spaces. More... »

PAGES

1-7

References to SciGraph publications

  • 1990-10. Uniqueness of unconditional bases in quasi-banach spaces with applications to Hardy spaces in ISRAEL JOURNAL OF MATHEMATICS
  • 1966-12. On perfectly homogeneous bases in Banach spaces in ISRAEL JOURNAL OF MATHEMATICS
  • 1971-09. On orlicz sequence spaces in ISRAEL JOURNAL OF MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1155/2009/865371

    DOI

    http://dx.doi.org/10.1155/2009/865371

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1034453083


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