Automatic surjectivity of ring homomorphisms on -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 -classes of an -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 , no quotient ring of is isomorphic to , a statement we conjecture to be true for every pair of group rings corresponding to different exponents .

**[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,*-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 -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 -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