Proceedings of the Japan Academy, Series A, Mathematical Sciences

On an ad hoc computability structure in a Hilbert space

Atsushi Yoshikawa

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Abstract

Pour-El & Richards [3] discussed an ad hoc computability structure in an effectively separable Hilbert space taking as an effective generating set a slightly modified one from the original orthonormal basis. We show that an application of the Poincaré-Wigner orthogonalizing procedure to Pour-El & Richards' modified system gives an orthonormal effective generating set which yields a third computability structure.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 3 (2003), 65-70.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116443645

Digital Object Identifier
doi:10.3792/pjaa.79.65

Mathematical Reviews number (MathSciNet)
MR1967048

Zentralblatt MATH identifier
1052.03039

Subjects
Primary: 03Dxx: Computability and recursion theory
Secondary: 46Axx: Topological linear spaces and related structures {For function spaces, see 46Exx}

Keywords
Computability structure effectively separable Hilbert space

Citation

Yoshikawa, Atsushi. On an ad hoc computability structure in a Hilbert space. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 3, 65--70. doi:10.3792/pjaa.79.65. https://projecteuclid.org/euclid.pja/1116443645


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References

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  • Pour-El, Marian B., and Richards, J. Ian: Computability in Analysis and Physics. Springer-Verlag, Berline-Heidelberg (1989).