### 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 language | English |
---|---|

Pages (from-to) | 85-96 |

Number of pages | 12 |

Journal | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |

Volume | 105 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2011 |

Externally published | Yes |

### Fingerprint

### 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

**Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space.** / Wegner, Sven Ake.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space

AU - Wegner, Sven Ake

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - PLB-space

KW - Tensor product of a Fréchet and a DF-space

KW - Weighted spaces of continuous functions

UR - http://www.scopus.com/inward/record.url?scp=79952609329&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952609329&partnerID=8YFLogxK

U2 - 10.1007/s13398-011-0001-2

DO - 10.1007/s13398-011-0001-2

M3 - Article

VL - 105

SP - 85

EP - 96

JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

SN - 1578-7303

IS - 1

ER -