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Homology and cohomology for topological algebras. (English) Zbl 0271.46040


MSC:

46H05 General theory of topological algebras
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
47A60 Functional calculus for linear operators
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46M99 Methods of category theory in functional analysis
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References:

[1] Cartan, H.; Eilenberg, S., Homological Algebra (1956), Princeton University Press: Princeton University Press Princeton · Zbl 0075.24305
[2] Guichardet, A., Sur ĺ’homologie et la cohomologie des algèbres de Banach, C. R. Acad. Sci. Paris Ser. A, 262, 38-41 (1966) · Zbl 0131.13101
[3] Guichardet, A., Sur l’homologie et la cohomologie des groupes localement compacts, C. R. Acad. Sci. Paris Ser. A, 262, 118-120 (1966) · Zbl 0131.13102
[4] Grothendieck, A., Sur les espaces \((F)\) et (DF), Summa Brasil. Math., 3, 57-123 (1954) · Zbl 0058.09803
[5] Grothendieck, A., Espaces vectoriels topologiques (1958), Instituto de Matematica Pura e Aplicado, Universidade de São Paulos · Zbl 0058.33401
[6] Grothendieck, A., Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc., No. 16 (1955) · Zbl 0064.35501
[7] Hochschild, G., On the cohomology groups of an associative algebra, Ann. of Math., 46, 58-67 (1945) · Zbl 0063.02029
[8] Hochschild, G., On the chomology theory for associative algebras, Ann. of Math., 47, 568-579 (1946) · Zbl 0063.02030
[9] Johnson, B. E., The Wedderburn decomposition of Banach algebras with finite dimensional radical, Amer. J. Math., 90, 866-876 (1968) · Zbl 0175.43904
[10] B. E. Johnson; B. E. Johnson
[11] Kadison, R. V.; Ringrose, J. R., Cohomology of operators algebras I, Type I von Neumann algebras, Acta Math., 126, 227-243 (1971) · Zbl 0209.44501
[12] Kamowitz, H., Cohomology groups of commutative Banach algebras, Trans. Amer. Math. Soc., 102, 352-372 (1962) · Zbl 0114.31703
[13] MacLane, S., Homology (1967), Springer-Verlag: Springer-Verlag New York · Zbl 0133.26502
[14] Nachbin, L., A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc., 68, 28-46 (1950) · Zbl 0035.35402
[15] Schaefer, H., Topological Vector Spaces (1966), Macmillan: Macmillan New York · Zbl 0141.30503
[16] Taylor, J. L., A joint spectrum for several commuting operators, J. Functiona Analysis, 6, 172-191 (1970) · Zbl 0233.47024
[17] Taylor, J. L., The analytic functional calculus for several commuting operators, Acta Math., 125, 1-38 (1970) · Zbl 0233.47025
[18] Taylor, J. L., Several variable spectral theory, (Wilde, Functional Analysis (1970), Academic Press: Academic Press NY) · Zbl 0295.47001
[19] Taylor, J. L., A general framework for a multi-operator functional calculus, Advances in Mathematics, 9, 183-252 (1972) · Zbl 0271.46041
[20] Treves, F., Topological Vector Spaces, Distributions, and Kernels (1967), Academic Press: Academic Press NY · Zbl 0171.10402
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