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Interpolation in Separable Frechet Spaces with Applications to Spaces of Analytic Functions

Published online by Cambridge University Press:  20 November 2018

Paul M. Gauthier  and
Lee A. Rubel
Paul M. Gauthier
Affiliation:
Université de Montréal, Montreal, Quebec; University of Illinois at Urbana-Champaign, Urbana, Illinois
Lee A. Rubel
Affiliation:
Université de Montréal, Montreal, Quebec; University of Illinois at Urbana-Champaign, Urbana, Illinois
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Let E be a separable Fréchet space, and let E* be its topological dual space. We recall that a Fréchet space is, by definition, a complete metrizable locally convex topological vector space. A sequence {Ln} of continuous linear functional is said to be interpolating if for every sequence {An} of complex numbers, there exists an ƒ ∈ E such that Ln(ƒ) = An for n = 1, 2, 3, … . In this paper, we give necessary and sufficient conditions that {Ln} be an interpolating sequence. They are different from the conditions in [2] and don't seem to be easily interderivable with them.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1110 - 1113
Copyright
Copyright © Canadian Mathematical Society 1975

References

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