Functiones et Approximatio Commentarii Mathematici

Tame (PLS)-spaces

Krzysztof Piszczek

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Abstract

The class of (PLS)-spaces covers most of the natural spaces of analysis, e. g. the space of real analytic functions, spaces of distributions. We characterize those (PLS)-spaces for which there exists a 'reasonable' (LFS)-topology, i. e. a topology of the inductive limit of a sequence of Fréchet-Schwartz spaces. Then we characterize - in terms of the defining sequence - power series (PLS)-type spaces which satisfy the same condition. It is known that power series (PLS)-type spaces appear naturally as kernels of convolution operators.

Article information

Source
Funct. Approx. Comment. Math., Volume 38, Number 1 (2008), 67-80.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229624652

Digital Object Identifier
doi:10.7169/facm/1229624652

Mathematical Reviews number (MathSciNet)
MR2433789

Zentralblatt MATH identifier
1194.46001

Subjects
Primary: 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40] 46A63: Topological invariants ((DN), ($\Omega$), etc.) 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]

Keywords
Fréchet space (PLS)-space (LFS)-space

Citation

Piszczek, Krzysztof. Tame (PLS)-spaces. Funct. Approx. Comment. Math. 38 (2008), no. 1, 67--80. doi:10.7169/facm/1229624652. https://projecteuclid.org/euclid.facm/1229624652


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