Continuous and Smooth Envelopes of Topological Algebras. Part 2

Journal of Mathematical Sciences - Tập 227 Số 6 - Trang 669-789 - 2017
S. S. Akbarov1
1Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, Moscow, Russia

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J. Adámek and J. Rosicky, Locally Presentable and Accessible Categories, Cambridge Univ. Press (1994).

S. S. Akbarov, “Pontryagin duality in the theory of topological vector spaces and in topological algebra,” J. Math. Sci., 113, No. 2, 179–349 (2003).

S. S. Akbarov, “Holomorphic functions of exponential type and duality for Stein groups with algebraic connected component of identity,” J. Math. Sci., 162, No. 4, 459–586 (2009); http://arxiv.org/abs/0806.3205 .

S. S. Akbarov, “Envelopes and refinements in categories, with applications to functional analysis,” Diss. Math., 513, No. 1, 1–188, (2016); http://arxiv.org/abs/1110.2013 .

D. V. Alexeevski, A. M. Vinogradov, and V. V. Lychagin, Basic Ideas and Concepts of Differential Geometry, Springer-Verlag (1991).

O. Yu. Aristov, “Characterization of strict C*-algebras,” Stud. Math., 112, No. 1, 51–58 (1994).

O. Yu. Aristov, “On tensor products of strict C*-algebras,” Fundam. Prikl. Mat., 6, No. 4, 977–984 (2000).

V. A. Artamonov, V. N. Salij, L. A. Skornjakov, L. N. Shevrin, and E. G. Shulgeifer, General Algebra [in Russian], Nauka, Moscow (1991).

A. Barut and R. Raczka, Theory of Group Representations and Applications, World Scientific (1986).

T. Becker, “A few remarks on the Dauns–Hofmann theorems for C*-algabras,” Arch. Math., 43, 265–269 (1984).

J. Bochnak, M. Coste, and M.-F. Roy, Real Algebraic Geometry, Springer-Verlag (1998).

F. Borceux, Handbook of Categorical Algebra. 1. Basic Category Theory, Cambridge Univ. Press (1994).

N. Bourbaki, Elements of Mathematics. Topological Vector Spaces, Springer-Verlag (2002).

I. Bucur and A. Deleanu, Introduction to the Theory of Categories and Functors, Wiley (1968).

A. H. Clifford, “Representations induced in an invariant subgroup,” Ann. Math., 38, No. 3, 533–550 (1937).

C. Chevalley, Theory of Lie Groups, Princeton Univ. Press (1946).

A. Connes, Noncommutative Geometry, Academic Press, Boston, MA (1994).

J. B. Cooper, Saks Spaces and Applications to Functional Analysis, North Holland Math. Stud. 139, Elsevier (1987).

J. Dauns and K. H. Hofmann, “Representations of rings by continuous sections,” Mem. Am. Math. Soc., 83 (1968).

J. Dixmier, Les C*-Algébres et Leurs Reprèsentations, Gauthier (1969).

M. J. Duprè and R. M. Gillette, Banach Bundles, Banach Modules, and Automorphisms of C*-Algebras, Res. Notes Math., 92, Boston (1983).

R. Engelking, General Topology, PWN, Warszawa (1977).

M. Enock and J.-M. Schwartz, Kac Algebras and Duality of Locally Compact Groups, Springer-Verlag (1992).

P. Eymard, “L’algèbre de Fourier d’un groupe localement compact,” Bull. Soc. Math. Fr., 92, 181–236 (1964).

M. Fragoulopoulou, Topological Algebras with Involution, North-Holland (2005).

H. Freudenthal, “Einige Sätze über topologische Gruppen,” Ann. Math., 37, No. 2, 46–56 (1936).

H. Grauert and R. Remmert, Theory of Stein Spaces, Springer-Verlag (1977).

P. Griffiths and J. Harris, Principles of Algebraic Geometry, Vols. 1, 2, Wiley (1994).

S. Grosser and M. Moskowitz, “On central topological groups,” Trans. Am. Math. Soc., 127, No. 2, 317–340 (1967).

S. Grosser and M. Moskowitz, “Compactness conditions in topological groups,” J. Reine Angew. Math., 246, 1–40 (1971).

E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer-Verlag (1994).

E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. II, Springer-Verlag (1994).

A. Hulanicki, “Groups whose regular representation weakly contains all unitary representations,” Stud. Math., 24, 37–59 (1964).

J. E. Humphreys, Linear Algebraic Groups, Springer-Verlag (1975).

H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart (1981).

R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. I, Academic Press (1986).

R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. II, Academic Press (1986).

J. L. Kelley, Van NostrandGeneral Topology, (1957).

E. Kowalski, Representation Theory, ETH Zürich (2011).

A. Kriegl and P. W. Michor, The Convenient Setting of Global Analysis, Am. Math. Soc. (1997).

Yu. Kuznetsova, “A duality for Moore groups,” J. Oper. Theory, 69, No. 2, 101–130 (2013); http://arxiv.org/abs/0907.1409 .

J. G. Llavona, Approximation of Continuously Differentiable Functions, North Holland (1986).

D. Luminet and A. Valette, “Faithful uniformly continuous representations of Lie groups,” J. London Math. Soc., 49, No. 2, 100–108 (1994).

S. MacLane. Categories for the Working Mathematician, Springer-Verlag, Berlin (1971).

S. Majid, Foundations of Quantum Group Theory, Cambridge Univ. Press (1995).

P. W. Michor, Topics in Differential Geometry, Grad. Stud. Math., Vol. 93, Am. Math. Soc., Providence (2008).

G. J. Murphy, C*-Algebras and Operator Theory, Academic Press (1990).

L. Nachbin, “Sur les algèbres denses de fonctions diffèrentiables sur une variété,” C. R. Acad. Sci. Paris, 228, 1549–1551 (1949).

T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. II, Academic Press (2001).

A. L. T. Paterson, Amenability, Math. Surv. Monogr., 29 (1988).

I. G. Petrovsky, Lectures on the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1964).

A. Yu. Pirkovskii, “Arens–Michael envelopes, homological epimorphisms, and relatively quasi-free algebras,” Tr Mosk. Mat. Obshch., 69, 34–123 (2008).

A. Pietsch, Nuclear Locally Convex Spaces, Springer-Verlag (1972).

M. M. Postnikov, Lie Groups and Lie Algebras, Mir, Moscow (1986).

J. Renault, “Fourier-algebra (2),” in: Encycl. Math. (M. Hazewinkel, ed.), Springer-Verlag (2001).

H. Rossi, “On envelops of holomorphy,” Commun. Pure Appl. Math., 16, 9–17 (1963).

Z. Sebestyén, “Every C*-seminorm is automatically submultiplicative,” Period. Math. Hung., 10, 1–8 (1979).

I. M. Singer, “Uniformly continuous representations of Lie groups,” Ann. Math. (2), 56, 242–247 (1952).

H. H. Shaeffer, Topological Vector Spaces, Macmillan (1966).

R. W. Sharpe, Differential Geometry. Cartan’s Generalization of Klein’s Erlangen Program, Springer-Verlag (1997).

A. I. Shtern, “Norm continuous representations of locally compact groups,” Russ. J. Math. Phys., 15, No. 4, 552–553 (2008).

J. L. Taylor, Several Complex Variables with Connections to Algebraic Geometry and Lie Groups, Grad. Stud. Math., 46, Am. Math. Soc., Providence, Rhode Island (2002).

J. L. Taylor, “Homology and cohomology for topological algebras,” Adv. Math., 9, 137–182 (1972).

M. S. Tsalenko and E. G. Shulgeifer, Foundations of Category Theory [in Russian], Nauka (1974).

A. L. Onishchik and E. B. Vinberg, Lie Groups and Algebraic Groups, Springer-Verlag (1990).

D. Zhelobenko, Principal Structures and Methods of Representation Theory, Am. Math. Soc. (2006).