Skip to main content
Log in

Tensor products of power Köthe spaces of different types

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

The multirectangular characteristics µ (λ,c) m are applied to the isomorphic classification of tensor products of the form \( E_0 (a)\widehat \otimes E_\infty (b) \). We single out a subclass of tensor products such that the two-rectangular characteristic µ (λ,c)2 is a complete invariant on this class.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Meise and D. Vogt, Introduction to Functional Analysis, in Oxford Grad. Texts Math. (Oxford Univ. Press, New York, 1997), Vol. 2.

    Google Scholar 

  2. M. M. Dragilev, Bases in Köthe space (Izd. Rostov. Univ., Rostov-on-Don, 1983) [in Russian].

    Google Scholar 

  3. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, in Mem. Amer. Math. Soc. (Amer. Math. Soc., Providence, RI, 1955), Vol. 16.

    Google Scholar 

  4. V. P. Zahariuta, “Linear topological invariants and their application to generalized power spaces,” Turkish J. Math. 20(2), 237–289 (1996).

    MathSciNet  MATH  Google Scholar 

  5. B. S. Mityagin, “Approximative dimension and bases in nuclear spaces,” Funktsional. Anal. i Prilozhen. 16(4), 63–132 (1961) [Functional Anal. Appl. 16 (4), 59–128 (1961)].

    Google Scholar 

  6. A. Pietsch, Nukleare lokalkonvexe Räume, in Schriftenreihe der Institute für Mathematik bei der Deutschen Akademie der Wissenschaften zu Berlin. Reihe A, Reine Mathematik, Heft 1 (Akademie-Verlag, Berlin, 1965).

    Google Scholar 

  7. V. P. Zakharyuta, “On the isomorphism and quasiequivalence of bases for power Köthe spaces,” in Proc. of the 7th Winter Workshop in Mathematical Programming and Related Questions, Drogobych, 1974 (TSÉMI, Moscow, 1976), pp. 101–126 [in Russian].

    Google Scholar 

  8. H. Schaefer, Topological Vector Spaces (Macmillan, New York, 1966; Mir, Moscow, 1971).

    MATH  Google Scholar 

  9. P. A. Chalov, T. Terzioğlu, and V. P. Zahariuta, “First-type power Köthe spaces and m-rectangular invariants,” in Linear Topol. Spaces Complex Anal. (Sci. Tech. Res. Council Turkey, Ankara, 1997), Vol. 3, pp. 30–44.

    Google Scholar 

  10. M. Hall, Combinatorial Theory (Blaisdell-Ginn, Waltham, Mass.-Toronto, Ont.-London, 1967; Mir, Moscow, 1970).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. A. Chalov.

Additional information

Original Russian Text © P. A. Chalov, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 4, pp. 629–635.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chalov, P.A. Tensor products of power Köthe spaces of different types. Math Notes 83, 573–578 (2008). https://doi.org/10.1134/S0001434608030310

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434608030310

Key words

Navigation