Stability of the van der Waerden theorem on the continuity of homomorphisms of compact semisimple Lie groups

Applied Mathematics and Computation

Volumn 187, Issue 1 SPEC. ISS., 2007, Pages 455-465

  Shtern, A I ^a,b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Amenable Banach algebra; Compact semisimple Lie group; Continuous representation; Group representation; Quasi representation; Topological group; Unitary representation; Van der Waerden continuity theorem

Indexed keywords

BANACH SPACES; SPECTRUM ANALYSIS; TOPOLOGY;

CONTINUOUS REPRESENTATION; GROUP REPRESENTATION; QUASI REPRESENTATION; UNITARY REPRESENTATION; VAN DER WAERDEN THEOREM;

FUNCTIONAL ANALYSIS;

EID: 34247471139     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.08.145     Document Type: Article

References (44)

1. Bavard C. Longueur stable des commutateurs. L'Enseignement Mathématique 37 (1991) 109-150
2. Biran P., Entov M., and Polterovich L. Calabi quasimorphisms for the symplectic ball. Commun. Contemp. Math. 6 5 (2004) 793-802
3. de la Harpe P., and Karoubi M. Représentations approchées d'un groupe dans une algèbre de Banach. Manuscripta Math. 22 3 (1977) 297-310
4. Dunford N., and Schwartz J.T. Linear Operators I (1958), Interscience, New York
5. Gaal S.A. Linear Analysis and Representation Theory (1973), Springer-Verlag, New York-Heidelberg
6. Gambaudo J.-M., and Ghys E. Commutators and diffeomorphisms of surfaces. Ergodic Theory Dyn. Syst. 24 5 (2004) 1591-1617
7. Greenleaf F.P. Invariant Means on Topological Groups and their Applications (1969), Van Nostrand Reinhold Co., New York-Toronto, Ont.-London
8. Gromov M. Positive curvature, macroscopic dimension, spectral gaps and higher signatures. Functional Analysis on the Eve of the 21st Century vol. II (1996), Dordrecht, Boston, MA 1-213
9. Grove K., Karcher H., and Ruh E.A. Jacobi fields and Finsler metrics on a compact Lie groups with an application to differential pinching problems. Math. Ann. 211 1 (1974) 7-21
10. Helgason S. Differential Geometry and Symmetric Spaces (1962), Academic, New York
11. Hewitt E., and Ross K.A. Abstract Harmonic Analysis I (1979), Springer-Verlag, Berlin-New York
12. Hofmann K.H., and Morris S.A. The Structure of Compact Groups (1998), de Gruyter, Berlin-New York
13. Jarosz K. Perturbations of Banach algebras. Lecture Notes in Mathematics vol. 1120 (1985), Springer-Verlag, Berlin-New York
14. Johnson B.E. Cohomology in Banach Algebras. Mem. Amer. Math. Soc. vol. 127 (1972), American Mathematical Society, Providence, RI
15. Johnson B.E. Approximate diagonals and cohomology of certain annihilator Banach algebras. Amer. J. Math. 94 (1972) 685-698
16. Johnson B.E. Approximately multiplicative functionals. J. Lond. Math. Soc. (2) 34 3 (1986) 489-510
17. Johnson B.E. Continuity of generalized homomorphisms. Bull. Lond. Math. Soc. 19 1 (1987) 67-71
18. Johnson B.E. Approximately multiplicative maps between Banach algebras. J. Lond. Math. Soc. (2) 37 2 (1988) 294-316
19. Johnson B.E. Perturbations of multiplication and homomorphisms, deformation theory of algebras and structures and applications (Il Ciocco, 1986). Info NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 247 (1988), Kluwer Acad. Publ., Dordrecht pp. 565-579
20. Kazhdan D. On ε-representations. Israel J. Math. 43 4 (1982) 315-323
21. Kotschick D. What is ... a quasi-morphism?. Notices Amer. Math. Soc. 51 2 (2004) 208-209
22. Manning J.F. Geometry of pseudocharacters. Geom. Topol. 9 (2005) 1147-1185
23. McDuff D. A survey of the topological properties of symplectomorphism groups. Topology, Geometry and Quantum Field Theory. Info Lond. Math. Soc. Lecture Note Ser. 308 (2004), Cambridge Univ. Press, Cambridge 173-193
24. Naimark M.A., and Štern [Shtern] A.I. Theory of Group Representations (1982), Springer-Verlag, New York-Heidelberg-Berlin
25. Paterson A.L.T. Amenability (1988), Amer. Math. Soc., Providence, RI
26. Radical Banach algebras and automatic continuity, in: John M. Bachar, William G. Bade, Philip C. Curtis, Jr., H. Garth Dales, Marc P. Thomas (Eds.), Info Proceedings of the Conference held at California State University, Long Beach, CA, 17-31 July 1981, Lecture Notes in Mathematics, vol. 975, Springer-Verlag, Berlin-New York, 1983.
27. Shtern A.I. Stability of representations and pseudocharacters. Lomonossov Readings (1983), Moscow State University, Moscow
28. Shtern A.I. A pseudocharacter that is determined by the Rademacher symbol. Uspekhi Mat. Nauk 45 3(273) (1990) 197-198
29. Shtern A.I. Quasireprezentations and pseudorepresentations. Funkts. Analiz i eqo Prilo-zhen. 25 2 (1991) 70-73
30. Shtern A.I. Quasi-symmetry. I. Russ. J. Math. Phys. 2 3 (1994) 353-382
31. Shtern A.I. Characterizations of amenable groups in the class of connected locally compact groups. Uspekhi Mat. Nauk 49 2(296) (1994) 183-184
32. Shtern A.I. Triviality and continuity of pseudocharacters and pseudorepresentations. Russ. J. Math. Phys. 5 1 (1997) 135-138
33. Shtern A.I. Roughness and approximation of quasi-representations of amenable groups. Mat. Zametki 65 6 (1999) 908-920
34. Shtern A.I. Structure properties and the bounded real continuous 2-cohomology of locally compact groups. Funkts. Analiz i eqo Prilo-zhen. 35 4 (2001) 67-80
35. Shtern A.I. Remarks on pseudocharacters and the real continuous bounded cohomology of connected locally compact groups. Ann. Global Anal. Geom. 20 (2001) 199-221
36. Shtern A.I. A criterion for the second real continuous bounded cohomology of a locally compact group to be finite-dimensional. Acta Appl. Math. 68 1-3 (2001) 105-121
37. Shtern A.I. Criteria for weak and strong continuity of representations of topological groups in Banach spaces (Russian). Mat. Sb. 193 9 (2002) 139-156
38. Shtern A.I. Deformation of irreducible unitary representations of a discrete series of Hermitian symmetric simple Lie groups in the class of pure pseudo-representations (Russian). Mat. Zametki 73 3 (2003) 478-480
39. Shtern A.I. Criteria for the continuity of finite-dimensional representations of connected locally compact groups. Mat. Sb. 195 9 (2004) 145-159
40. Shtern A.I. Projective representations and pure pseudorepresentations of Hermitian symmetric simple Lie groups. Mat. Zametki 77 6 (2005) 908-913
41. Shtern A.I. Automatic continuity of pseudocharacters on Hermitian symmetric semisimple Lie groups. Adv. Stud. Contemp. Math. (Kyungshang) 12 1 (2006)
42. A.I. Shtern, Strong and weak continuity of representations of topologically pseudocomplete groups in locally convex spaces, in press.
43. Takesaki M. Theory of Operator Algebras I (1979), Springer-Verlag, New York
44. van der Waerden B.L. Stetigkeitssätze für halbeinfache Liesche Gruppen. Math. Z. 36 (1933) 780-786