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On symmetric algebras. (English) Zbl 0938.46048

The author studies various concepts of symmetry in *-algebras both in a purely algebraic context as well as in the context of locally multiplicatively convex Fréchet algebras.

MSC:

46K05 General theory of topological algebras with involution
46H05 General theory of topological algebras

Citations:

Zbl 0927.00014
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Full Text: DOI

References:

[1] B. A. Barnes, ”Algebras with the spectral expansion property,”Illinois J. Math.,11, 284–290 (1967). · Zbl 0148.37504
[2] D. G. Birbas, ”Pták function and symmetry,”Rend. Circ. Mat. di Palermo, to appear. · Zbl 0926.46043
[3] F. F. Bonsall and J. Duncan, ”Numerical ranges,” In:MAA Studies in Mathematics, Vol. 21. · Zbl 0461.47001
[4] P. G. Dixon, ”Automatic continuity of positive functionals on topological involution algebras,”Bull. Austr. Math. Soc.,23, 265–281 (1981). · Zbl 0453.46046 · doi:10.1017/S0004972700007127
[5] R. S. Doran and V. A. Belfi,Characterizations of C *-algebras. The Gel’fand-Naimark Theorems, Marcel Dekker (1986). · Zbl 0597.46056
[6] M. Fragoulopoulou, ”An introduction to the representation theory of topological *-algebras,” In:Schriftenreihe des Math. Institut der Univ. Münster, Vol. 48 (1988). · Zbl 0653.46058
[7] M. Fragoulopoulou, ”Symmetric topological *-algebras. Applications,” In:Schriftrenreihe des Math. Institut der Univ. Münster, Vol. 3. Serie 9 (1993). · Zbl 0811.46054
[8] M. Fragoulopoulou, ”Tensor products of enveloping locally C*-algebras,” In:Schriftrenreihe des Math. Institut der Univ. Münsterto appear. · Zbl 0906.46040
[9] M. Haralampidou, ”Annihilator topological algebras,”Portugaliae Math.,51, 147–162 (1994). · Zbl 0806.46051
[10] A. Mallios,Topological Algebras. Selected Topics, North-Holland, Amsterdam (1986). · Zbl 0597.46046
[11] E. A. Michael, ”Locally multiplicatively-convex topological algebras,”Mem. Amer. Math. Soc., No. 11 (1952). · Zbl 0047.35502
[12] T. W. Palmer, ”Hermitian Banach *-algebras,”Bull. Amer. Math. Soc.,78, 522–524 (1972). · Zbl 0255.46045 · doi:10.1090/S0002-9904-1972-12980-X
[13] T. W. Palmer, ”*-Representations ofU *-algebras,”Indiana Univ. Math. J.,20, No. 10, 929–933 (1971). · Zbl 0209.44402 · doi:10.1512/iumj.1971.20.20082
[14] T. W. Palmer,Banach Algebras and the General Theory of *-Algebras, Vol. 1Encyclopedia of Mathematics and Its Applications, Cambridge University Press (1994). · Zbl 0809.46052
[15] V. Pták, ”Banach algebras with involution,”Manuscr. Math.,6, 245–290 (1972). · Zbl 0229.46054 · doi:10.1007/BF01304613
[16] C. E. Rickart,General Theory of Banach Algebras, R. E. Krieger Publ. Co., Huntington, New York (1974). · Zbl 0275.46045
[17] Z. Sebestyén, ”States and *-representations I,”Period. Math. Hung.,17, 163–176 (1986). · Zbl 0624.46035 · doi:10.1007/BF01848645
[18] Z. Sebestyén, ”On representability of linear functionals on *-algebras,”Period. Math. Hung.,15, 233–239 (1984). · Zbl 0567.46027 · doi:10.1007/BF02454172
[19] Y. Tsertos, ”Representations and extensions of positive functionals on *-algebras,”Bollettino U. M. I., (7)8-B, 541–555 (1994). · Zbl 0834.46038
[20] J. Wichmann, ”The symmetric radical of an algebra with involution,”Arch. Math. (Basel),30, 83–88 (1978). · Zbl 0399.16007
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