Cocycles and local product decomposition

Tanaka, Jun-ichi

doi:10.1090/S0002-9947-1983-0701511-6

Cocycles and local product decomposition
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by Jun-ichi Tanaka

Trans. Amer. Math. Soc. 278 (1983), 565-572

DOI: https://doi.org/10.1090/S0002-9947-1983-0701511-6

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Abstract:

As an application of cocycles, we establish a relation between the classical Hardy spaces on the real line $R$ and simply invariant subspaces on a quotient of the Bohr group. When this result is specialized suitably, it yields the well-known results concerning the elements of invariant subspaces. We also study, by using Gamelin’s representation theorem, unitary functions which are the values of cocycles.

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