On commutative V*-algebras II
Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 129-134

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We show that the commutative V*-algebras with relatively weakly compact unit spheres are those that are representable by means of hermitian spectral measures. This provides a more unified approach to the results of [15], and allows us to generalise some of them.
Spain, P. G. On commutative V*-algebras II. Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 129-134. doi: 10.1017/S0017089500001531
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[1] 1.Bartle, R. G., Dunford, N. and Schwartz, J. T., Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289–305. Google Scholar | DOI

[2] 2.Berkson, E., A characterization of scalar type operators on reflexive Banach spaces, Pacific J. Math. 13 (1963), 365–373. Google Scholar | DOI

[3] 3.Berkson, E., Some characterizations of C*-algebras, Illinois J. Math. 10 (1966), 1–8. Google Scholar | DOI

[4] 4.Berkson, E., Action of W*-algebras in Banach spaces, Math. Ann. 189 (1970), 261–271. Google Scholar | DOI

[5] 5.Berkson, E. and Dowson, H. R., Prespectral operators, Illinois J. Math. 13 (1969), 291–315. Google Scholar | DOI

[6] 6.Dixmier, J., Les algèbres d'opérateurs dans l'espace hilbertien (Paris, 1957). Google Scholar

[7] 7.Dunford, N. and Schwartz, J. T., Linear operators (New York, 1958 and 1963). Google Scholar

[8] 8.Edward, D. A. and Tulcea, C. T. Ionescu, Some remarks on commutative algebras of operators on Banach spaces, Trans. Amer. Math. Soc. 93 (1959), 541–551. Google Scholar | DOI

[9] 9.Grothendieck, A., Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129–173. Google Scholar | DOI

[10] 10.Lumer, G., Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29–43. Google Scholar | DOI

[11] 11.Palmer, T. W., Characterizations of C*-algebras, Bull. Amer. Math. Soc. 74 (1968), 538–540. Google Scholar | DOI

[12] 12.Palmer, T. W., Unbounded normal operators on Banach spaces, Trans. Amer. Math. Soc. 133 (1968), 385–414. Google Scholar | DOI

[13] 13.Panchapagesan, T. V., Semigroups of scalar type operators in Banach spaces, Pacific J. Math. 30 (1969), 489–517. Google Scholar | DOI

[14] 14.Ringrose, J. R., Lecture notes on von Neumann algebras (Newcastle upon Tyne, 1967). Google Scholar

[15] 15.Spain, P. G., On commutative V*-algebras, Proc. Edinburgh Math. Soc. (2) 17 (1970), 173–180. Google Scholar | DOI

[16] 16.Spain, P. G., V*-algebras with weakly compact unit spheres, J. London Math. Soc. (2) 4 (1971), 62–64. Google Scholar | DOI

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