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Pták function and symmetry. (English) Zbl 0926.46043
Summary: 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.

46K05 General theory of topological algebras with involution
46K10 Representations of topological algebras with involution
Full Text: DOI
[1] Barnes B. A.,Algebras with the spectral expansion property, J. Math.11 (1967), 284–290. · Zbl 0148.37504
[2] 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. · Zbl 0812.46049
[3] Doran R. S., Belfi V. A.,Characterizations of C *-algebras. The Gelfand-Naimark Theorems. Marcell-Dekker, 1986. · Zbl 0597.46056
[4] Fragoulopoulou M.,An introduction to the representation theory of topological *-algebras, Schriftenreihe des Math. Intituts der Univ. Munster,48 (1988). · Zbl 0653.46058
[5] Fragoulopoulou M.,Symmetric topological *-algebras. Applications Schriftrenreihe des Math. Instituts der Univ. Müster, 3. Serie,9 (1993). · Zbl 0811.46054
[6] Mallios A.,Topological Algebras. Selected Topics, North-Holland, Amsterdam, 1986. · Zbl 0597.46046
[7] Müller V.,Normed alebras with involution, Manuscripta Math.75 no 2 (1992), 197–210. · Zbl 0781.46041
[8] Palmer T.W.,The Gel’fand-Naimark pseudo-norm on Banach *-algebras, J. London Math. Soc. (2),3 (1971), 59–66. · Zbl 0207.44304
[9] Palmer T.W.,*-Representations of U*-algebras, Indiana University Math. J. vol. 20 No.10 (1971), 929–933. · Zbl 0209.44402
[10] Palmer T.W.,Banach Algebras as and the General Theory d’Algebras, vol. I., Encyclopedia of Mathematics and its Applications, Cambridge, University Press, 1994.
[11] Palmer T.W.,The reducing ideal is a radical, Pacific J. Math. vol. 43 No.1 (1972), 207–219. · Zbl 0248.46045
[12] Pták V.,Banach algebras with involution, Manuser. Math.6 (1972), 245–290. · Zbl 0229.46054
[13] Rickart C. E.,General Theory of Banach Algebras, R. E. Krieger Publ. Co. Huntington New York, 1974. · Zbl 0275.46045
[14] Tsertos Y.,Representation and Extension of Positive Functionals on *-Algebras, Bollettino U.M.I. (7)8-B (1994), 541-SS5. · Zbl 0834.46038
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