Uncountable chains and antichains of varieties of Banach algebras. (English) Zbl 0807.46050
A variety of Banach algebras is a nonempty class of Banach algebras closed under taking closed subalgebras, quotient algebras, products and images under isometric isomorphisms. The purpose of this paper is to study the structure of the lattice of all varieties of Banach algebras: upper and lower bounds, chains, etc.
Reviewer: H.Hogbe Nlend (Bordeaux)
MSC:
| 46H05 | General theory of topological algebras |
Keywords:
subalgebras; quotient algebras; products; images under isometric isomorphisms; lattice of all varieties of Banach algebrasReferences:
| [1] | Cohn, P. M., Universal Algebra (1965), Harper & Row: Harper & Row New York · Zbl 0141.01002 |
| [2] | Dixon, P. G., Varieties of Banach algebras, Quart. J. Math. Oxford Ser. (2), 27, 481-487 (1976) · Zbl 0338.46045 |
| [3] | Dixon, P. G., A characterization of closed subalgebras of \(B(H)\), (Proc. Edinburgh Math. Soc. (2), 20 (1976-1977)), 215-217 · Zbl 0347.46074 |
| [4] | Sz-Nagy, B.; Foias, C., Harmonic Analysis of Operators on Hilbert Spaces (1970), North-Holland: North-Holland Amsterdam · Zbl 0201.45003 |
| [5] | Sz-Nagy, B., Unitary dilations of Hilbert space operators and related topics, (CBMS Regional Conf. Ser. in Math., 19 (1974)) · Zbl 0281.47004 |
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