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This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which...
The structure of closed ideals of a regular algebra containing the classical A∞ is considered. Several division and approximation results are proved and a characterization of those ideals whose intersection with A∞ is not {0} is obtained. A complete description of the ideals with countable hull is given, with applications to synthesis of hyperfunctions.
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