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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
Published electronically: June 30, 1999
MathSciNet review: 1616645
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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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Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P. O. Box 12, Hungary

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