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Proceedings of the American Mathematical Society

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Affine invariant subspaces of $ C({\bf C})$


Authors: Yaki Sternfeld and Yitzhak Weit
Journal: Proc. Amer. Math. Soc. 107 (1989), 231-236
MSC: Primary 46E10
DOI: https://doi.org/10.1090/S0002-9939-1989-0979053-3
MathSciNet review: 979053
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Abstract: A linear subspace $ A$ of $ C({\mathbf{C}})$ is affine invariant if $ f(z) \in A$ implies that $ f(az + b) \in A$ for every $ a,b \in {\mathbf{C}}$.

We present a classification of the affine invariant closed subspaces of $ C({\mathbf{C}})$, and of those affine invariant subspaces which are also composition invariant (i.e., $ f,g \in A$ implies that $ f \circ g \in A)$).


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DOI: https://doi.org/10.1090/S0002-9939-1989-0979053-3
Article copyright: © Copyright 1989 American Mathematical Society

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