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On homeomorphisms of the unit circle preserving orientation

Published online by Cambridge University Press:  22 January 2016

Masaru Hara
Masaru Hara*
Affiliation:
Mathematical Institute, Division of General Education at Faculty of Science and Engineering, Meijô University
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Let Γ denote the unit circle in the complex plane C, C(Γ) the set of complex valued continuous functions on Γ which is a Banach space by the sup-norm ‖·‖, A(z) the uniform closure of all polynomials in z on Γ, H(Γ) the set of homeomorphisms of Γ, H+(Γ) the set of direction-preserving homeomorphisms and H−(Γ) the set of direction-reversing homeomorphisms. For ψ ∈ H(Γ), let A(ψ) denote the uniform closure of all polynomials in ψ on Γ.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 75 , September 1979 , pp. 87 - 94
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

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