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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The uniform continuity of certain translation semigroups
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by Jimmie Lee Johnson PDF
Proc. Amer. Math. Soc. 71 (1978), 197-203 Request permission

Abstract:

Let ${S_h}f(x) = f(x + h)$ for $h \geqslant 0$, for $f \in {L^2}({R^ + };K)$, where K is a separable Hilbert space. The translation semigroup ${S_h}$ when restricted to an invariant subspace L is uniformly continuous if and only if ${G_L}$ is an inner function and has an analytic continuation across an open arc of the unit circle at $z = 1$. The operator-valued function ${G_L}$ is associated with the invariant subspace L by Beurling’s theorem.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 197-203
  • MSC: Primary 47D05; Secondary 47A15
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0512908-5
  • MathSciNet review: 0512908