Bulletin of the Belgian Mathematical Society - Simon Stevin

On a property of PLS-spaces inherited by their tensor products

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 investigate the property of PLS-spaces called {\it dual interpolation estimate} and show that in many important and classical cases this property is inherited by tensor products of two PLS-spaces. We establish the inheritance if at least one of the spaces is a nuclear Fréchet space or a PLN-space. The latter includes the important, classical case when one of the spaces is the dual of a nuclear Fréchet space.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 1 (2010), 155-170.

Dates
First available in Project Euclid: 5 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1267798505

Mathematical Reviews number (MathSciNet)
MR2656678

Zentralblatt MATH identifier
1205.46002

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] 46A32: Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
Secondary: 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46M05: Tensor products [See also 46A32, 46B28, 47A80] 47L05: Linear spaces of operators [See also 46A32 and 46B28]

Keywords
Fréchet-Schwartz space LS-space PLS-space nuclear space $(DN)-(\Omega)$ type conditions

Citation

Piszczek, Krzysztof. On a property of PLS-spaces inherited by their tensor products. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 1, 155--170. https://projecteuclid.org/euclid.bbms/1267798505


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