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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


$ H\sp{\infty }(R)+AP$ is closed

Author: Stephen Power
Journal: Proc. Amer. Math. Soc. 65 (1977), 73-76
MSC: Primary 46E15; Secondary 46J15
MathSciNet review: 0448047
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Abstract: Let $ {H^\infty }(R)$ be the space of functions on the real line R which are boundary functions of functions bounded and analytic in the upper half-plane and let AP denote the space of uniformly almost periodic functions on R. We show that $ {H^\infty }(R) + AP$ is closed and is not an algebra.

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PII: S 0002-9939(1977)0448047-0
Keywords: Analytic functions, uniformly almost periodic functions, invariant mean, Bochner-Fejér polynomials, Banach space
Article copyright: © Copyright 1977 American Mathematical Society