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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 5, Pages 1159–1174 (Mi izv1751)  

This article is cited in 14 scientific papers (total in 14 papers)

Biprojective Banach algebras

Yu. V. Selivanov


Abstract: This paper studies the structure of biprojective semisimple Banach algebras having the approximation property. It is shown that every such algebra can be represented as the completion of a direct sum of topologically simple biprojective Banach algebras. The component parts of this sum are described as algebras of nuclear operators generated by a dual pair. Furthermore, the closed ideals of such algebras are studied.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:2, 387–399

Bibliographic databases:

UDC: 513.88
MSC: Primary 46M10; Secondary 18G05, 46H25
Received: 14.11.1977

Citation: Yu. V. Selivanov, “Biprojective Banach algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 43:5 (1979), 1159–1174; Math. USSR-Izv., 15:2 (1980), 387–399

Citation in format AMSBIB
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\by Yu.~V.~Selivanov
\paper Biprojective Banach algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 5
\pages 1159--1174
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\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 2
\pages 387--399
\crossref{https://doi.org/10.1070/IM1980v015n02ABEH001249}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Ya. Helemskii, “Homological methods in Taylor's holomorphic calculus of several operators in a Banach space”, Russian Math. Surveys, 36:1 (1981), 139–192  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Ya. Helemskii, “The homological essence of Connes amenability: injectivity of the predual bimodule”, Math. USSR-Sb., 68:2 (1991), 555–566  mathnet  crossref  mathscinet  zmath  isi
    3. Niels Grønbaek, “Amenability and weak amenability of tensor algebras and algebras of nuclear operators”, J Austral Math Soc, 51:3 (1991), 483  crossref
    4. Yu. O. Golovin, “A criterion for the spatial projectivity of an indecomposable CSL-algebra of operators”, Russian Math. Surveys, 49:4 (1994), 161–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Yu. V. Selivanov, “Cohomology of Biflat Banach Algebras with Coefficients in Dual Bimodules”, Funct. Anal. Appl., 29:4 (1995), 289–291  mathnet  crossref  mathscinet  zmath  isi
    6. A. Ya. Helemskii, “Approximately finite-dimensional $C^*$-algebras with projective Hilbert modules, their Bratteli diagrams, and $K_0$-groups”, Sb. Math., 188:10 (1997), 1543–1560  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Vern I. Paulsen, “Relative Yoneda Cohomology for Operator Spaces”, Journal of Functional Analysis, 157:2 (1998), 358  crossref
    8. R.J. Loy, C.J. Read, V. Runde, G.A. Willis, “Amenable and Weakly Amenable Banach Algebras with Compact Multiplication”, Journal of Functional Analysis, 171:1 (2000), 78  crossref
    9. Yu. V. Selivanov, “Lower bounds for homological dimensions of Banach algebras”, Sb. Math., 198:9 (2007), 1351–1377  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. A. Ya. Helemskii, “Projective modules in the classical and quantum functional analysis”, J. Math. Sci., 159:5 (2009), 600–652  mathnet  crossref  mathscinet  zmath  elib  elib
    11. O. Yu. Aristov, “Structure of biprojective Banach algebras with non-trivial radical”, Izv. Math., 72:6 (2008), 1111–1140  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. NIELS GRØNBÆK, FEREIDOUN HABIBIAN, “BIFLATNESS AND BIPROJECTIVITY OF Banach ALGEBRAS GRADED OVER A SEMILATTICE”, Glasgow Math J, 52:3 (2010), 479  crossref
    13. A. Yu. Pirkovskii, “Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras”, Izv. Math., 76:4 (2012), 702–759  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. S. B. Tabaldyev, “Additivity of homological dimensions for tensor products of some Banach algebras”, Moscow University Mathematics Bulletin, 69:4 (2014), 164–168  mathnet  crossref  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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