Algebraic difference between 𝑝-classes of an H*-algebra

Molnár, Lajos

doi:10.1090/S0002-9939-96-03048-1

Algebraic difference between $p$-classes of an H*-algebra
HTML articles powered by AMS MathViewer

by Lajos Molnár

Proc. Amer. Math. Soc. 124 (1996), 169-175

DOI: https://doi.org/10.1090/S0002-9939-96-03048-1

PDF | Request permission

Abstract:

We show that there do not exist surjective ring homomorphisms between different $p$-classes of an infinite-dimensional H*-algebra.

References

J. Aczél and J. Dhombres, Functional equations in several variables, Encyclopedia of Mathematics and its Applications, vol. 31, Cambridge University Press, Cambridge, 1989. With applications to mathematics, information theory and to the natural and social sciences. MR 1004465, DOI 10.1017/CBO9781139086578
P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
Albert Eagle, Series for all the roots of a trinomial equation, Amer. Math. Monthly 46 (1939), 422–425. MR 5, DOI 10.2307/2303036
Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR 0423029, DOI 10.1007/978-3-642-65669-9
R. W. Cross, On the continuous linear image of a Banach space, J. Austral. Math. Soc. Ser. A 29 (1980), no. 2, 219–234. MR 566287, DOI 10.1017/S1446788700021200
I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
Marek Kuczma, An introduction to the theory of functional equations and inequalities, Prace Naukowe Uniwersytetu Śląskiego w Katowicach [Scientific Publications of the University of Silesia], vol. 489, Uniwersytet Śląski, Katowice; Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1985. Cauchy’s equation and Jensen’s inequality; With a Polish summary. MR 788497
Jeanne LaDuke, On a certain generalization of ${\cal l}_{p}$ spaces, Pacific J. Math. 35 (1970), 155–168. MR 275139, DOI 10.2140/pjm.1970.35.155
Lajos Molnár, ${}^\ast$-representations of the trace-class of an $H^*$-algebra, Proc. Amer. Math. Soc. 115 (1992), no. 1, 167–170. MR 1110549, DOI 10.1090/S0002-9939-1992-1110549-X
Lajos Molnár, $p$-classes of an $H^*$-algebra and their representations, Acta Sci. Math. (Szeged) 58 (1993), no. 1-4, 411–423. MR 1264246
Matjaž Omladič and Peter emrl, Additive mappings preserving operators of rank one, Linear Algebra Appl. 182 (1993), 239–256. MR 1207085, DOI 10.1016/0024-3795(93)90502-F
Parfeny P. Saworotnow and John C. Friedell, Trace-class for an arbitrary $H^{\ast }$-algebra, Proc. Amer. Math. Soc. 26 (1970), 95–100. MR 267402, DOI 10.1090/S0002-9939-1970-0267402-9
Parfeny P. Saworotnow, Trace-class and centralizers of an $H^{\ast }$-algebra, Proc. Amer. Math. Soc. 26 (1970), 101–104. MR 267403, DOI 10.1090/S0002-9939-1970-0267403-0
Parfeny P. Saworotnow and George R. Giellis, Continuity and linearity of centralizers on a complemented algebra, Proc. Amer. Math. Soc. 31 (1972), 142–146. MR 288585, DOI 10.1090/S0002-9939-1972-0288585-2
Parfeny P. Saworotnow, Generalized positive definite functions and stationary processes, Prediction theory and harmonic analysis, North-Holland, Amsterdam-New York, 1983, pp. 329–343. MR 708534
Parfeny P. Saworotnow, Diagonalization of a selfadjoint operator acting on a Hilbert module, Internat. J. Math. Math. Sci. 8 (1985), no. 4, 669–675. MR 821622, DOI 10.1155/S0161171285000734
Peter emrl, Additive derivations of some operator algebras, Illinois J. Math. 35 (1991), no. 2, 234–240. MR 1091440
Peter emrl, Ring derivations on standard operator algebras, J. Funct. Anal. 112 (1993), no. 2, 318–324. MR 1213141, DOI 10.1006/jfan.1993.1035
Peter emrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1851–1855. MR 1242104, DOI 10.1090/S0002-9939-1995-1242104-8
James F. Smith, The $p$-classes of an $H^{\ast }$-algebra, Pacific J. Math. 42 (1972), 777–793. MR 322517, DOI 10.2140/pjm.1972.42.777
Pak Ken Wong, The $p$-class in a dual $B^{\ast }$-algebra, Trans. Amer. Math. Soc. 200 (1974), 355–368. MR 358371, DOI 10.1090/S0002-9947-1974-0358371-X