Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space

Sven Ake Wegner

Research output: Contribution to journalArticle

Abstract

Countable projective limits of countable inductive limits, so-called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen et al., who analyzed locally convex properties in terms of the defining double sequence of weights. We complement their results by considering a defining sequence which is the product of two single sequences. By associating these two sequences with a weighted Fréchet, resp. LB-space of continuous functions or with two weighted Fréchet spaces (by taking the reciprocal of one of the sequences) we derive a representation of the PLB-space as the tensor product of a Fréchet and a DF-space and exhibit a connection between the invariants (DN) and (Ω) for Fréchet spaces and locally convex properties of the PLB-space resp. of the forementioned tensor product.

Original languageEnglish
Pages (from-to)85-96
Number of pages12
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume105
Issue number1
DOIs
Publication statusPublished - Mar 2011
Externally publishedYes

Fingerprint

Spaces of Continuous Functions
Weighted Spaces
Tensor Product
Tensors
Banach spaces
Countable
Projective Limit
Double Sequences
Inductive Limit
Complement
Banach space
Invariant

Keywords

  • PLB-space
  • Tensor product of a Fréchet and a DF-space
  • Weighted spaces of continuous functions

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Geometry and Topology

Cite this

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