Skip to main content
SpringerLink
Log in

The boundedness principle for lattice-normed spaces

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

The three classical facts of the theory of normed spaces are considered: the boundedness principle, the Banach-Steinhaus theorem, and the uniform boundedness principle for a compact convex set. By means of Boolean valued analysis, the analogs of the theorems are proven in a lattice-normed space setting.

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. Kusraev A. G., Dominated Operators, Kluwer Academic Publishers, Dordrecht (2001).

    Google Scholar 

  2. Kusraev A. G. and Kutateladze S. S., Introduction to Boolean Valued Analysis [in Russian], Nauka, Moscow (2005).

    Google Scholar 

  3. Ganiev I. G. and Kudajbergenov K. K., “Banach-Steinhaus uniform boundedness principle for operators in Banach-Kantorovich spaces over L 0,” Mat. Tr., 9, No. 1, 21–33 (2006).

    MathSciNet  Google Scholar 

  4. Gutman A. E., “Banach bundles in the theory of lattice-normed spaces,” in: Linear Operators Coordinated with Order [in Russian], Institute of Mathematics, Novosibirsk, 1995, pp. 63–211.

    Google Scholar 

  5. Kutateladze S. S., Fundamentals of Functional Analysis, Kluwer Academic Publishers, Dordrecht etc. (1995).

    Google Scholar 

  6. Rudin W., Functional Analysis, McGraw-Hill, New York, etc. (1991).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. E. Gutman

  2. Novosibirsk State University, Novosibirsk, Russia

    S. A. Lisovskaya

Authors
  1. A. E. Gutman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Lisovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Gutman.

Additional information

To Academician Yu. G. Reshetnyak on his eightieth birthday.

Original Russian Text Copyright © 2009 Gutman A. E. and Lisovskaya S. A.

__________

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 5, pp. 1050–1059, September–October, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gutman, A.E., Lisovskaya, S.A. The boundedness principle for lattice-normed spaces. Sib Math J 50, 830–837 (2009). https://doi.org/10.1007/s11202-009-0093-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-009-0093-5

Keywords

Search

Navigation