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Prehermitian elements and \(B^*\)-algebras. (English) Zbl 0215.48503

MSC:

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

[1] Behncke, H.: A note on the Gelfand-Naimark conjecture. Comm. Pure and Appl. Math.23, 189-200 (1970). · Zbl 0188.44601 · doi:10.1002/cpa.3160230206
[2] Berkson, E.: Some types of Banach spaces, hermitian operators, and Bade functionals. Trans. Amer. Math. Soc.116, 376-385 (1965). · Zbl 0135.36502 · doi:10.1090/S0002-9947-1965-0187100-2
[3] ?? Some characterizations ofC*-algebras. Ill. J. Math.10, 1-8 (1966).
[4] Cleveland, S. B.: Homomorphisms of non-commutative *-algebras. Pacific J. Math.13, 1097-1109 (1963). · Zbl 0205.42203
[5] Lumer, G.: Semi-inner-product spaces. Trans. Amer. Math. Soc.100, 29-43 (1961). · Zbl 0102.32701 · doi:10.1090/S0002-9947-1961-0133024-2
[6] ?? Spectral operators, hermitian operators, and bounded groups. Acta Sci. Math.25, 75-85 (1964). · Zbl 0168.12103
[7] Palmer, T. W.: Characterizations ofC*-algebras. Bull. A.M.S.74, 538-540 (1968). · Zbl 0159.18503 · doi:10.1090/S0002-9904-1968-11998-6
[8] – The Gelfand-Naimark pseudo-norm on Banach *-algebras, accepted for publication by London Math. Soc.
[9] Rickart, C.: General theory of Banach algebras. New York: Van Nostrand 1960. · Zbl 0095.09702
[10] Shirali, S., Ford, J. W. M.: Symmetry in complex involutory Banach algebras, II. Duke Math. J.37, 275-280 (1970). · Zbl 0183.14202 · doi:10.1215/S0012-7094-70-03735-X
[11] Vidav, I.: Eine metrische Kennzeichnung der selbstadjungierten Operatoren. Math. Zeitschr.66, 121-128 (1956). · Zbl 0071.11503 · doi:10.1007/BF01186601
[12] Yood, B.: On axioms forB*-algebras. Bull. A.M.S.76, 80-82 (1970). · Zbl 0188.44602 · doi:10.1090/S0002-9904-1970-12371-0
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