Skip to main content
SpringerLink
Log in

Embedding of Stein spaces into sequence spaces

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this note we show that a connected, reduced Stein space X of arbitrary dimension admits a holomorphic embedding into various sequence spaces, for example into s,s',0(ℂn) or ℂ<T1,T2,...,Tn>, and also into infinite dimensional complex Banach spaces. As an application we prove that the Fréchet space 0 (X) of holomorphic functions on X is a quotient of s.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • BÖRGENS,M., MEISE,R. and VOGT,D.: Entire functions on nuclear function spaces. J. Reine Angew. Math.322, 196–220 (1981)

    Google Scholar 

  • BUNGART,L.: Holomorphic functions with values in locally convex spaces and ... Trans. Amer. Math. Soc.111, 317–344 (1964)

    Google Scholar 

  • GUNNING,R.C., ROSSI,H.: Analytic functions of several variables. Prentice-Hall, Englewood Cliffs, N.J. 1965

    Google Scholar 

  • LINDENSTRAUSS,J., TZAFRIRI,L.: Classical Banach spaces I. Ergebnisse 92, Springer, Berlin 1977

    Google Scholar 

  • MAZET,P.: Un theorèm d'image propre. Sam. P. Lelong 1972/73 and 1973/74. Lecture Notes in Mathematics410 and474. Springer, Berlin 1974 and 1975.

    Google Scholar 

  • NARASIMHAN,R.: Imbedding of holomorphically complete complex spaces. Amer. J. Math.82, 917–934 (1960)

    Google Scholar 

  • NOSSKE,D.: Forthcoming dissertation (München)

  • SCHOTTENLOHER,M.: Michael problem and algebras of holomorphic functions. Arch. Math.37, 241–247 (1981)

    Google Scholar 

  • VOGT,D.: Subspaces and quotient spaces of (s). In: Functional Analysis: Surveys and Results. (Ed.) Bierstedt, K.D., Fuchssteiner,B.) North-Holland, Amsterdam 1977. pp. 167–187

    Google Scholar 

  • WIEGMANN,K.W.: Einbettung komplexer Räume in Zahlenräume. Invent. math.1, 229–242 (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, der Universität München, Theresienstraße 39, D-8000, München 2

    Martin Schottenloher

Authors
  1. Martin Schottenloher
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schottenloher, M. Embedding of Stein spaces into sequence spaces. Manuscripta Math 39, 15–29 (1982). https://doi.org/10.1007/BF01312442

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01312442

Keywords

Search

Navigation