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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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

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

First available in Project Euclid: 18 May 2005

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Zentralblatt MATH identifier

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

Computability structure effectively separable Hilbert space


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.

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