Representations of locally convex $^{\ast }$-algebras
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- by James D. Powell PDF
- Proc. Amer. Math. Soc. 44 (1974), 341-346 Request permission
Abstract:
Conditions for a functional to be admissible on a locally convex $\ast$-algebra are defined. Let $F$ be an admissible positive Hermitian functional on a commutative locally convex $\ast$-algebra; then it is shown that there exists a representation of $A$ into a Hilbert space. Sufficient conditions for a functional $F$ to be representable are also given.References
- G. R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. (3) 15 (1965), 399–421. MR 176344, DOI 10.1112/plms/s3-15.1.399
- G. R. Allan, On a class of locally convex algebras, Proc. London Math. Soc. (3) 17 (1967), 91–114. MR 205102, DOI 10.1112/plms/s3-17.1.91
- Ernest A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952), 79. MR 51444
- 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. MR 0115101
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 341-346
- MSC: Primary 46K10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0361803-X
- MathSciNet review: 0361803