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On the Arens product and annihilator algebras. (English) Zbl 0218.46059

##### MSC:
 46L05 General theory of $$C^*$$-algebras 47L45 Dual algebras; weakly closed singly generated operator algebras 46H20 Structure, classification of topological algebras
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##### References:
 [1] Richard Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839 – 848. · Zbl 0044.32601 [2] Bruce A. Barnes, Modular annihilator algebras, Canad. J. Math. 18 (1966), 566 – 578. · Zbl 0156.04003 · doi:10.4153/CJM-1966-055-6 · doi.org [3] Robert C. Busby, Double centralizers and extensions of \?*-algebras, Trans. Amer. Math. Soc. 132 (1968), 79 – 99. · Zbl 0165.15501 [4] Paul Civin and Bertram Yood, The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11 (1961), 847 – 870. · Zbl 0119.10903 [5] Paul Civin, Ideals in the second conjugate algebra of a group algebra, Math. Scand. 11 (1962), 161 – 174. · Zbl 0178.16603 · doi:10.7146/math.scand.a-10663 · doi.org [6] Jacques Dixmier, Les \?*-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). · Zbl 0288.46055 [7] L. Terrell Gardner, On isomorphisms of \?*-algebras, Amer. J. Math. 87 (1965), 384 – 396. · Zbl 0139.30602 · doi:10.2307/2373010 · doi.org [8] George W. Mackey, Isomorphisms of normed linear spaces, Ann. of Math. (2) 43 (1942), 244 – 260. · Zbl 0061.24210 · doi:10.2307/1968868 · doi.org [9] Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. · Zbl 0095.09702 [10] B. J. Tomiuk and Pak-ken Wong, The Arens product and duality in \?*-algebras, Proc. Amer. Math. Soc. 25 (1970), 529 – 535. · Zbl 0198.17902 [11] Pak-ken Wong, The Arens product and duality in \?*-algebras. II, Proc. Amer. Math. Soc. 27 (1971), 535 – 538. · Zbl 0209.44404
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