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A general framwork for a multi-operator functional calculus. (English) Zbl 0271.46041

46H05 General theory of topological algebras
47A60 Functional calculus for linear operators
46M99 Methods of category theory in functional analysis
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
17B15 Representations of Lie algebras and Lie superalgebras, analytic theory
Full Text: DOI
[1] Arens, R; Calderon, A.P, Analytic functions of several Banach algebra elements, Ann. of math., 62, 204-216, (1955) · Zbl 0065.34802
[2] Cartan, H; Eilenberg, S, Homological algebra, Princeton math. series, (1956), Princeton, NJ · Zbl 0075.24305
[3] Chevalley, C, Theory of Lie groups, Princeton math. series, (1946), Princeton, NJ · Zbl 0063.00842
[4] Grothendieck, A, Products tensoriels topologiques et espaces nucleaires, Mem. amer. math. soc., 16, (1955) · Zbl 0064.35501
[5] Gunning, R.C; Rossi, H, Analytic functions of several complex variables, (1965), Prentice-Hall Englewood Cliffs, NJ · Zbl 0141.08601
[6] Helgason, S, Differential geometry and symmetric spaces, (1962), Academic Press New York · Zbl 0122.39901
[7] Iwasawa, K, On some types of topological groups, Ann. of math., 50, 507-558, (1949) · Zbl 0034.01803
[8] Koszul, L, Homologie et cohomologie des algèbres de Lie, Bull. soc. math. France, 78, 65-127, (1950) · Zbl 0039.02901
[9] MacLane, S, Homology, (1963), Springer-Verlag New York · Zbl 0133.26502
[10] Michael, E, Locally multiplicatively-convex topological algebras, Mem. amer. math. soc., 11, (1952) · Zbl 0047.35502
[11] Serre, J.P, Lie algebras and Lie groups, (1965), Benjamin New York
[12] Schaefer, H, Topological vector spaces, (1966), Macmillan New York · Zbl 0141.30503
[13] Shilov, G.E, On the decomposition of a normed ring into a direct sum of ideals, Amer. math. soc. transl., 1, 37-48, (1955) · Zbl 0066.36103
[14] Taylor, J.L, A joint spectrum for several commuting operators, J. functional anal., 6, 172-191, (1970) · Zbl 0233.47024
[15] Taylor, J.L, The analytic functional calculus for several commuting operators, Acta math., 125, 1-38, (1970) · Zbl 0233.47025
[16] Taylor, J.L, Several variable spectral theory, () · Zbl 0295.47001
[17] Taylor, J.L, Homology and cohomology for topological algebras, Advances in mathematics, 9, 137-182, (1972) · Zbl 0271.46040
[18] Treves, F, Topological vector spaces, distributions and kernels, (1967), Academic Press New York · Zbl 0171.10402
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