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Automatic surjectivity of ring homomorphisms on $H^{*}$-algebras and algebraic differences among some group algebras of compact groups


Author: Lajos Molnár
Journal: Proc. Amer. Math. Soc. 128 (2000), 125-134
MSC (1991): Primary 46K15, 47D50, 47B49; Secondary 43A15, 43A22
DOI: https://doi.org/10.1090/S0002-9939-99-04974-6
Published electronically: June 30, 1999
MathSciNet review: 1616645
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we present two automatic surjectivity results concerning ring homomorphisms between $p$-classes of an $H^{*}$-algebra which, in some sense, improve the main theorem in a recent paper by the author (Proc. Amer. Math. Soc. 124 (1996), 169-175) quite significantly. Furthermore, we apply our results to show that for arbitrary infinite compact groups $G,G'$, no quotient ring of $L^{2}(G)$ is isomorphic to $L^{p}(G')$ $(2<p\leq \infty )$, a statement we conjecture to be true for every pair $L^{p}(G), L^{q}(G')$ of group rings corresponding to different exponents $1\leq p,q\leq \infty $.


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  • [AD] J. Aczél and J. Dhombres, Functional Equations in Several Variables, Encyclopedia Math. Appl. 31, Cambridge University Press, 1989. MR 90h:39001
  • [Amb] W. Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364-386. MR 7:126c
  • [Arn] B.H. Arnold, Rings of operators on vector spaces, Ann. of Math. 45 (1944), 24-49. MR 5:147c
  • [Dra] D.D. Draghia, Continuitate in Algebre Banach, Editure didactica si pedagogica, Bucuresti, 1995.
  • [Eid] M. Eidelheit, On isomorphisms of rings of linear operators, Studia Math. 9 (1940), 97-105. MR 3:51e
  • [GK] I.C. Gohberg and M.G. Krein, Introduction to The Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs Vol. 18, American Mathematical Society, 1969. MR 39:7447
  • [HR] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis II., Springer-Verlag, 1970. MR 41:7378
  • [Kap] I. Kaplansky, Ring isomorphisms of Banach algebras, Canad. Math. J. 6 (1954), 374-381. MR 16:49e
  • [Kuc] M. Kuczma, An Introduction to The Theory of Functional Equations and Inequalities, Pa\'{n}stwowe Wydawnictwo Naukowe, Warszawa, 1985. MR 86i:39008
  • [Mol1] L. Molnár, $p$-classes of an H*-algebra and their representations, Acta Sci. Math. (Szeged) 58 (1993), 411-423. MR 95c:46081
  • [Mol2] L. Molnár, Algebraic difference between $p$-classes of an H*-algebra, Proc. Amer. Math. Soc. 124 (1996), 169-175. MR 96d:46072
  • [Mol3] L. Molnár, The range of a ring homomorphism from a commutative $C^{*}$-algebra, Proc. Amer. Math. Soc. 124 (1996), 1789-1794. MR 96h:46090
  • [New] J.D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. MR 14:481b
  • [SF] P.P. Saworotnow and J.C. Friedell, Trace-class for an arbitrary H*-algebra, Proc. Amer. Math. Soc. 26 (1970), 95-100. MR 42:2304
  • [SG] P.P. Saworotnow and G.R. Giellis, Continuity and linearity of centralizers on a complemented algebra, Proc. Amer. Math. Soc. 31 (1972), 142-146. MR 44:5781
  • [Sem] P. \v{S}emrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), 1851-1855. MR 95g:47066

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Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P. O. Box 12, Hungary
Email: molnarl@math.klte.hu

DOI: https://doi.org/10.1090/S0002-9939-99-04974-6
Keywords: Ring homomorphism, $H^{*}$-algebra, $p$-class, compact group, group algebra, automatic surjectivity
Received by editor(s): March 4, 1997
Received by editor(s) in revised form: March 10, 1998
Published electronically: June 30, 1999
Additional Notes: This paper was completed when the author, holding a Hungarian State Eötvös Scholarship, was a visitor at the University of Maribor, Slovenia. This research was supported also by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T–016846 F–019322.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society

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