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ON THE COMPLEXITY OF CLASSIFYING LEBESGUE SPACES

Part of: Normed linear spaces and Banach spaces; Banach lattices Computability and recursion theory

Published online by Cambridge University Press:  26 October 2020

TYLER A. BROWN ,
TIMOTHY H. MCNICHOLL  and
ALEXANDER G. MELNIKOV
TYLER A. BROWN
Affiliation:
DEPARTMENT OF MATHEMATICS IOWA STATE UNIVERSITYAMES, IOWA50011, USA DIVISION OF HEALTH, MATHEMATICS, AND SCIENCES COLUMBIA COLLEGECOLUMBIA, SOUTH CAROLINA29203, USAE-mail: tbrown@columbiasc.edu
TIMOTHY H. MCNICHOLL
Affiliation:
DEPARTMENT OF MATHEMATICS IOWA STATE UNIVERSITYAMES, IOWA50011, USAE-mail: mcnichol@iastate.edu
ALEXANDER G. MELNIKOV
Affiliation:
THE INSTITUTE OF NATURAL AND MATHEMATICAL SCIENCES PRIVATE BAG 102 904 NSMC ALBANY 0745, AUCKLAND, NEW ZEALANDE-mail: alexander.g.melnikov@gmail.com
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Abstract

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

Keywords

computable analysiscomputable structure theoryLpspaces

MSC classification

Primary: 03D45: Theory of numerations, effectively presented structures
Secondary: 03D78: Computation over the reals 46B04: Isometric theory of Banach spaces
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 1254 - 1288
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Copyright
© The Association for Symbolic Logic 2020

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Footnotes

Part of this research was conducted while T. McNicholl visited A. Melnikov. This visit was funded by Marsden Fund of New Zealand and by Simons Foundation Grant # 317870.

References

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