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Generalized interpolation in finite maximal subdiagonal algebras

Published online by Cambridge University Press:  24 October 2008

Kichi-Suke Saito
Kichi-Suke Saito
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950–21, Japan
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Extract

Non-selfadjoint operator algebras have been studied since the paper of Kadison and Singer in 1960. In [1], Arveson introduced the notion of subdiagonal algebras as the generalization of weak *-Dirichlet algebras and studied the analyticity of operator algebras. After that, we have many papers about non-selfadjoint algebras in this direction: nest algebras, CSL algebras, reflexive algebras, analytic operator algebras, analytic crossed products and so on. Since the notion of subdiagonal algebras is the analogue of weak *-Dirichlet algebras, subdiagonal algebras have many fruitful properties from the theory of function algebras. Thus, we have several attempts in this direction: Beurling–Lax–Halmos theorem for invariant subspaces, maximality, factorization theorem and so on.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 11 - 20
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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