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 |
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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.
In: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Vol. 105, No. 1, 03.2011, p. 85-96.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 -