Abstract
We investigate subadditivity of Pták function as a sufficient and necessary condition for symmetry in the class of involutive spectrally bounded algebras. Among others it is proved an analogue of Raikov's criterion for complete lmc*-algebras in which the hermitian elements have finite spectral radius.
Similar content being viewed by others
References
Barnes B. A.,Algebras with the spectral expansion property, J. Math.11 (1967), 284–290.
Bhatt S. J., Karia D. J.,Topological algebras with C *-enveloping algebras, Proc. Indian Acad. Sci. (Math. Sci.) Vol.102 N. 3 (1992), 201–215.
Doran R. S., Belfi V. A.,Characterizations of C *-algebras. The Gelfand-Naimark Theorems. Marcell-Dekker, 1986.
Fragoulopoulou M.,An introduction to the representation theory of topological *-algebras, Schriftenreihe des Math. Intituts der Univ. Munster,48 (1988).
Fragoulopoulou M.,Symmetric topological *-algebras. Applications Schriftrenreihe des Math. Instituts der Univ. Müster, 3. Serie,9 (1993).
Mallios A.,Topological Algebras. Selected Topics, North-Holland, Amsterdam, 1986.
Müller V.,Normed alebras with involution, Manuscripta Math.75 no 2 (1992), 197–210.
Palmer T.W.,The Gel'fand-Naimark pseudo-norm on Banach *-algebras, J. London Math. Soc. (2),3 (1971), 59–66.
Palmer T.W.,*-Representations of U*-algebras, Indiana University Math. J. vol. 20 No.10 (1971), 929–933.
Palmer T.W.,Banach Algebras as and the General Theory d'Algebras, vol. I., Encyclopedia of Mathematics and its Applications, Cambridge, University Press, 1994.
Palmer T.W.,The reducing ideal is a radical, Pacific J. Math. vol. 43 No.1 (1972), 207–219.
Pták V.,Banach algebras with involution, Manuser. Math.6 (1972), 245–290.
Rickart C. E.,General Theory of Banach Algebras, R. E. Krieger Publ. Co. Huntington New York, 1974.
Tsertos Y.,Representation and Extension of Positive Functionals on *-Algebras, Bollettino U.M.I. (7)8-B (1994), 541-SS5.
Author information
Authors and Affiliations
Additional information
This paper is based on the author's Doctoral Thesis, University of Athens, written under the supervision of Professor M. Fragoulopoulou.
Rights and permissions
About this article
Cite this article
Birbas, D.G. Pták function and symmetry. Rend. Circ. Mat. Palermo 47, 431–446 (1998). https://doi.org/10.1007/BF02851390
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02851390