Affine invariant subspaces of c(c)

Yaki Sternfeld; Yitzhak Weit

doi:10.1090/S0002-9939-1989-0979053-3

Affine invariant subspaces of c(c)

Yaki Sternfeld, Yitzhak Weit

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A linear subspace A of C(C) is affine invariant if f(z) ∈ A implies that f(az + b) ∈ A for every a, b ∈ C. We present a classification of the affine invariant closed subspaces of C(C), and of those affine invariant subspaces which are also composition invariant (i.e., f, g ∈ A implies that f o g ∈ A).

Original language	English
Pages (from-to)	231-236
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	107
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1989-0979053-3
State	Published - Sep 1989

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1989-0979053-3

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abstract = "A linear subspace A of C(C) is affine invariant if f(z) ∈ A implies that f(az + b) ∈ A for every a, b ∈ C. We present a classification of the affine invariant closed subspaces of C(C), and of those affine invariant subspaces which are also composition invariant (i.e., f, g ∈ A implies that f o g ∈ A).",

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AB - A linear subspace A of C(C) is affine invariant if f(z) ∈ A implies that f(az + b) ∈ A for every a, b ∈ C. We present a classification of the affine invariant closed subspaces of C(C), and of those affine invariant subspaces which are also composition invariant (i.e., f, g ∈ A implies that f o g ∈ A).

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Affine invariant subspaces of c(c)

Abstract

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