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The second duals of certain spaces of analytic functions

Published online by Cambridge University Press:  09 April 2009

L. A. Rubel  and
A. L. Shields
L. A. Rubel
Affiliation:
University of Illinois
A. L. Shields
Affiliation:
University of Michigan
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Let ϕ be a continuous, decreasing, real-valued funtion on 0 ≦ r ≦ 1 with ϕ(1) = 0 and ϕ(r) > 0 for r < 1. Let E0 be the Banach space of analytic function f on the open unit disc D, such that f(z)φ(|z|) → 0 as |z| → 1, with norm , where we write ϕ(z) = ϕ(z) for z ∈ D. Let E be the Banach space of analytic functions f on D for which fφ is bounded in D, with the same norm as E0. It is easy to see that E is complete in this norm, and that E0 is a closed subspace of E.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 276 - 280
Copyright
Copyright © Australian Mathematical Society 1970

References

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