Structure theorems for a special class of Banach algebras
Author:
Warren Ambrose
Journal:
Trans. Amer. Math. Soc. 57 (1945), 364-386
MSC:
Primary 46.3X
DOI:
https://doi.org/10.1090/S0002-9947-1945-0013235-8
MathSciNet review:
0013235
Full-text PDF Free Access
References | Similar Articles | Additional Information
- [I] Albert, A. A., Structure of algebras, Amer. Math. Soc. Colloquium Publications, vol. 24, 1939.
- [II] Banach, S., Théorie des opérations linéaires, Warsaw, 1932.
- [III] I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726
- [IV] I. Gelfand and M. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 197–213 (English, with Russian summary). MR 0009426
- [V] Gottfried Köthe, Abstrakte Theorie nichtkommutativer Ringe mit einer Anwendung auf die Darstellungstheorie kontinuierlicher Gruppen, Math. Ann. 103 (1930), no. 1, 545–572 (German). MR 1512637, https://doi.org/10.1007/BF01455710
- [VI] F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, https://doi.org/10.2307/1968693
- [VII] Riesz, F., Über die linearen Transformationen des komplexen Hilbertschen Raumes, Acta Univ. Szeged. vol. 5 (1930-1932) pp. 23-54.
- [VIII] I. E. Segal, The group ring of a locally compact group. I, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 348–352. MR 4633, https://doi.org/10.1073/pnas.27.7.348
- [IX] -, Ring properties of certain classes of functions, Dissertation, Yale, 1940.
- [X] van der Waerden, B. L., Moderne Algebra, Berlin, 1931.
- [XI] Weil, A., L'Integration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, No. 869, 1940.
- [XII] J. H. M. Wedderburn, Algebras which do not possess a finite basis, Trans. Amer. Math. Soc. 26 (1924), no. 4, 395–426. MR 1501287, https://doi.org/10.1090/S0002-9947-1924-1501287-1
Retrieve articles in Transactions of the American Mathematical Society with MSC: 46.3X
Retrieve articles in all journals with MSC: 46.3X
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1945-0013235-8
Article copyright:
© Copyright 1945
American Mathematical Society