Norms of inner derivations for multiplier algebras of C-algebras and group C-algebras

Journal of Functional Analysis - Tập 262 - Trang 2050-2073 - 2012
Robert J. Archbold1, Eberhard Kaniuth2, Douglas W.B. Somerset1
1Institute of Mathematics, University of Aberdeen, Kingʼs College, Aberdeen AB24 3UE, Scotland, United Kingdom
2Institute of Mathematics, University of Paderborn, 33095 Paderborn, Germany

Tài liệu tham khảo

Alo, 1974, Normal Topological Spaces, vol. 65 Ara, 2003 Archbold, 1975, Density theorems for the centre of a C⁎-algebra, J. Lond. Math. Soc. (2), 10, 189, 10.1112/jlms/s2-10.2.189 Archbold, 1978, On the norm of an inner derivation of a C⁎-algebra, Math. Proc. Cambridge Philos. Soc., 84, 273, 10.1017/S0305004100055109 Archbold, 1987, Topologies for primal ideals, J. Lond. Math. Soc. (2), 36, 524, 10.1112/jlms/s2-36.3.524 Archbold, 1986, On factorial states of operator algebras, III, J. Operator Theory, 15, 53 Archbold, 1997, Simply connected nilpotent Lie groups with quasi-standard C⁎-algebras, Proc. Amer. Math. Soc., 125, 2733, 10.1090/S0002-9939-97-03830-6 Archbold, 2005, Stable rank and real rank for some classes of group C⁎-algebras, Trans. Amer. Math. Soc., 357, 2165, 10.1090/S0002-9947-05-03835-3 Archbold, 1990, Quasi-standard C⁎-algebras, Math. Proc. Cambridge Philos. Soc., 107, 349, 10.1017/S0305004100068614 Archbold, 1993, Transition probabilities and trace functions for C⁎-algebras, Math. Scand., 73, 81, 10.7146/math.scand.a-12458 Archbold, 2004, Inner derivations and primal ideals of C⁎-algebras, II, Proc. Lond. Math. Soc. (3), 88, 225, 10.1112/S002461150301431X Archbold, 2007, Measuring noncommutativity in C⁎-algebras, J. Funct. Anal., 242, 247, 10.1016/j.jfa.2006.06.012 Archbold, 2011, Multiplier algebras of C0(X)-algebras, Münster J. Math., 4, 73 R.J. Archbold, D.W.B. Somerset, Ideals in the multiplier and corona algebras of a C0(X)-algebra, J. Lond. Math. Soc., in press. Archbold, 1999, On the topology of the dual of a nilpotent Lie group, Math. Proc. Cambridge Philos. Soc., 125, 269, 10.1017/S0305004198003053 Baggett, 1981, The Hausdorff dual problem for connected groups, J. Funct. Anal., 43, 60, 10.1016/0022-1236(81)90037-9 Dauns, 1968, Representations of Rings by Continuous Sections, vol. 83 Delaroche, 1968, Sur les centres de C⁎-algebres, II, Bull. Sci. Math., 92, 111 Dixmier, 1960, Sur les représentations unitaires de groupes de Lie nilpotents, VI, Canad. J. Math., 12, 324, 10.4153/CJM-1960-028-6 Dixmier, 1968, Sur les espaces localement quasi-compact, Canad. J. Math., 20, 1093, 10.4153/CJM-1968-106-4 Dixmier, 1977 Dow, 1990, The space of minimal prime ideals of C(βN∖N) is probably not basically disconnected, vol. 123, 81 Dow, 1988, The space of minimal prime ideals of C(X) need not be basically disconnected, Proc. Amer. Math. Soc., 104, 317 Fell, 1960, The dual spaces of C⁎-algebras, Trans. Amer. Math. Soc., 94, 365 Fell, 1961, The structure of algebras of operator fields, Acta Math., 106, 233, 10.1007/BF02545788 Fell, 1964, Weak containment and induced representations. II, Trans. Amer. Math. Soc., 110, 424 Folland, 1995 Gillman, 1960 Glimm, 1960, A Stone–Weierstrass theorem for C⁎-algebras, Ann. of Math., 72, 216, 10.2307/1970133 Greenleaf, 1969 Grosser, 1971, Compactness conditions in topological groups, J. Reine Angew. Math., 246, 1 Harish-Chandra, 1952, Plancherel formula for the 2×2 real unimodular group, Proc. Natl. Acad. Sci. USA, 38, 337, 10.1073/pnas.38.4.337 Hewitt, 1963 Kadison, 1967, Derivations and automorphisms of operator algebras, II, J. Funct. Anal., 1, 204, 10.1016/0022-1236(67)90032-8 Kaniuth, 1979, Primitive ideal spaces of groups with relatively compact conjugacy classes, Arch. Math., 32, 16, 10.1007/BF01238463 Kaniuth, 2001, The Glimm ideal space of a two-step nilpotent locally compact group, Proc. Edinb. Math. Soc. (2), 44, 505, 10.1017/S0013091599001315 Kaniuth, 1995, Minimal primal and Glimm ideal spaces of group C⁎-algebras, J. Funct. Anal., 130, 45, 10.1006/jfan.1995.1063 Lazar, 2010, Quotient spaces determined by algebras of continuous functions, Israel J. Math., 179, 145, 10.1007/s11856-010-0075-0 Lee, 1977, Full algebras of operator fields trivial except at one point, Indiana Univ. Math. J., 26, 351, 10.1512/iumj.1977.26.26028 Losert, 2003, On the center of group C⁎-algebras, J. Reine Angew. Math., 554, 105 Milicic, 1971, Topological representation of the group C⁎-algebra of SL(2,R), Glas. Mat. Ser. III, 6, 231 Mosak, 1971, Central functions in group algebras, Proc. Amer. Math. Soc., 29, 613, 10.1090/S0002-9939-1971-0279602-3 Palmer, 2001 Pears, 1975 Pedersen, 1979 Somerset, 1993, The inner derivations and the primitive ideal space of a C⁎-algebra, J. Operator Theory, 29, 307 Somerset, 1994, Inner derivations and primal ideals of C⁎-algebras, J. Lond. Math. Soc. (2), 50, 568, 10.1112/jlms/50.3.568 Somerset, 1999, Minimal primal ideals in rings and Banach algebras, J. Pure Appl. Algebra, 144, 67, 10.1016/S0022-4049(98)00039-5 Stampfli, 1970, The norm of a derivation, Pacific J. Math., 33, 737, 10.2140/pjm.1970.33.737 Zsido, 1973, The norm of a derivation of a W⁎-algebra, Proc. Amer. Math. Soc., 38, 147