Proceedings of the Japan Academy

A note on the dilation theorems

Hiroshi Takai and Hiroaki Yamada

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Article information

Proc. Japan Acad., Volume 48, Number 4 (1972), 216-220.

First available in Project Euclid: 20 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A20: Dilations, extensions, compressions
Secondary: 46L99: None of the above, but in this section


Takai, Hiroshi; Yamada, Hiroaki. A note on the dilation theorems. Proc. Japan Acad. 48 (1972), no. 4, 216--220. doi:10.3792/pja/1195519699.

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  • [1] W. B. Arveson: Subalgebras of C*-algebras. Acta Math., 123, 141-224 (1969).
  • [2] C. Foias: La mesure Harmonique-spectrale et la theorie spectrale des operateurs generaux d'un espace de Hilbert. Bull. Soc. Math. France, 85, 263-282 (1957).
  • [3] M. A. Naimark: Normed Rings. Noordhoff, Groningen (1959).
  • [4] W. F. Stinespring: Positive functions on C*-algebras. Proc. Amer. Math. Soc, 6, 211-216 (1955).
  • [5] B. Sz. Nagy and C. Foias,: Harmonic Analysis of Operators on Hilbert Space. Akademiai Kiado, Budapest (1970).
  • [6] H. Umegaki: Positive definite functions and direct product of Hilbert spaces. Tohoku Math. J., 7, 206-211 (1955).

See also

  • Part II: Masahiro Nakamura, Hiroshi Takai. A note on the dilation theorems, II. Proc. Japan Acad., Volume 48, Number 5 (1972), 302--307.