Skip to main content
SpringerLink
Log in

Some topics on the continuation and smoothing of vector functions

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We consider problems of continuation of vector functions from a subspace to the entire space and of smoothing problems for these functions. It is shown that there exists a reflexive separable spaceX and a subspaceY such that even a very smooth mapping ofY does not extend to a uniformly continuous mapping of a neighborhood ofY.

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

  1. T. Figiel, J. Lindenstrauss, and V. D. Milman, “The dimension of almost spherical sections of convex bodies,”Acta Math.,139, Nos. 1–2, 53–94 (1977).

    MathSciNet  Google Scholar 

  2. I. G. Tsar'kov, “Global existence of an implicit function,”Mat. Sb. [Math. USSR-Sb.],184, No. 7, 79–116 (1993).

    MATH  Google Scholar 

  3. V. I. Berdyshev, “Continuity of the metric projection operator and its generalizations,” in:Constructive Function Theory '77 [in Russian], Sofia (1980), pp. 29–34.

  4. I. G. Tsar'kov, “Smoothing out uniformly continuous mappings inL p,”Mat. Zametki [Math. Notes],54, No. 3, 123–140 (1993).

    MATH  MathSciNet  Google Scholar 

  5. I. G. Tsar'kov, “Widths and the Jackson-type inequality for abstract functions,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],198, 219–231 (1992).

    MATH  MathSciNet  Google Scholar 

  6. A. F. Timan, “Deformation of metric spaces and related issues,”Uspekhi Mat. Nauk [Russian Math. Surveys],20, No. 2, 53–88 (1965).

    MATH  MathSciNet  Google Scholar 

  7. J. Lindenstrauss, “On non-linear projections in Banach spaces,”Michigan Math. J.,11, 263–287 (1964).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, USSR

    I. G. Tsar'kov

Authors
  1. I. G. Tsar'kov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 906–916, December, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsar'kov, I.G. Some topics on the continuation and smoothing of vector functions. Math Notes 58, 1327–1335 (1995). https://doi.org/10.1007/BF02304892

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02304892

Keywords

Search

Navigation