Pacific Journal of Mathematics

Biholomorphic maps in Hilbert space have a fixed point.

T. L. Hayden and T. J. Suffridge

Article information

Source
Pacific J. Math., Volume 38, Number 2 (1971), 419-422.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102970053

Mathematical Reviews number (MathSciNet)
MR0305158

Zentralblatt MATH identifier
0229.47043

Subjects
Primary: 32A99: None of the above, but in this section
Secondary: 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]

Citation

Hayden, T. L.; Suffridge, T. J. Biholomorphic maps in Hilbert space have a fixed point. Pacific J. Math. 38 (1971), no. 2, 419--422. https://projecteuclid.org/euclid.pjm/1102970053


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References

  • [1] J. Cronin, Fixed Points and Topological Degree in NonlinearAnalysis,Amer. Math. Soc. Survey #11, (1964).
  • [2] C. J. Earle and R. S. Hamilton, A Fixed point theorem for holomorphic mappings, (to appear).
  • [3] L. A. Harris, Schwarz'slemma in normed linearspaces, Proc. Natl. Acad. Sci., U. S. A. 62 (4), (1969), 1014-1017.
  • [4] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ. 31 (1957).
  • [5] S. Kakutani, Topological properties of the unit sphere in Hilbert space, Proc. Imp. Acad. Tokyo 19 (1943), 269-271.
  • [6] R. S. Phillips, On symplectic mappings of contraction operators, Studia Math., 31 (1968), 15-27.