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Ideal structure of operator and measure algebras

Ward, J.A. (1983) Ideal structure of operator and measure algebras. Monatshefte für Mathematik, 95 (2). pp. 159-172.

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Let H denote a finite dimensional Hilbert space with subspace E. The set {Mathematical expression} is a subalgebra of B(H). A complete description of the ideal (two-sided, left and right) structure of J(E) is given. Let G denote a compact group with dual object ∑(G), and let σ be an element of ∑(G). The results concerning J(E) are applied to certain convolution subalgebras of M(G), the algebras having the property that the set of operators, μ(σ), where μ lies in the algebra, is of the form J(E). In particular, all the minimal two-sided and right ideals are listed. The technique used is an extension of one employed by Hewitt and Ross in [1] to study the closed ideals of some convolution subalgebras of M(G) which contain T(G).

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Springer-Verlag
Copyright: © 1983 Springer-Verlag.
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