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Definability in functional analysis

Published online by Cambridge University Press:  12 March 2014

José Iovino
José Iovino*
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA 15213, USA, E-mail: iovino+@andrew.cmu.edu
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Abstract

The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples.

We introduce the notion of definable real-valued function in functional analysis: a real-valued function f defined on a structure of functional analysis is definable if it can be “approximated” by formulas which do not involve f. We characterize definability of real-valued functions in terms of a purely topological condition which does not involve logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 2 , June 1997 , pp. 493 - 505
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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