Skip to main content
Log in

Calculating the global dimension of tensor products of Banach algebras and a generalization of Phillips' theorem

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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.

Literature cited

  1. A. Ya. Khelemskii, “The homological dimension of normed modules over Banach algebras,” Mat. Sb.,81, 430–444 (1970).

    Google Scholar 

  2. A. Grothendieck, “Produit tensoriels topologiques et espaces nucléaires,” Mem. Am. Math. Soc.,16, 3–191 (1955).

    Google Scholar 

  3. Yu. V. Selivanov, “Values taken by the global dimension in certain classes of Banach algebras,” Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh.,1, 37–42 (1975).

    Google Scholar 

  4. Yu. O. Golovin and A. Ya. Khelemskii, “The homological dimension of certain modules over tensor products of Banach algebras,” Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., 1, 54–61 (1977).

    Google Scholar 

  5. R. S. Phillips, “On linear transformations,” Trans. Am. Math. Soc.,48, No. 3, 516–541 (1940).

    Google Scholar 

  6. A. Ya. Khelemskii, “The least values taken by the global homological dimension of functional Banach algebras,” Tr. Sem. im. I. G. Petrovskogo, No. 3, 223–242 (1978).

    Google Scholar 

  7. A. Ya. Khelemskii, “A method of calculating and estimating the global dimension of Banach algebras,” Mat. Sb.,87, 125–135 (1972).

    Google Scholar 

  8. S. MacLane, Homology, Springer-Verlag, Berlin (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 31, No. 2, pp. 187–202, February, 1982.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krichevets, A.N. Calculating the global dimension of tensor products of Banach algebras and a generalization of Phillips' theorem. Mathematical Notes of the Academy of Sciences of the USSR 31, 95–104 (1982). https://doi.org/10.1007/BF01158128

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158128

Keywords

Navigation