A simple constructive proof of an analogue of the corona theorem

von Renteln, Michael

doi:10.1090/S0002-9939-1981-0624918-8

A simple constructive proof of an analogue of the corona theorem
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by Michael von Renteln

Proc. Amer. Math. Soc. 83 (1981), 299-303

DOI: https://doi.org/10.1090/S0002-9939-1981-0624918-8

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Abstract:

We present a simple and constructive proof (i.e. a proof without using Gelfand theory) of an analogue of the Corona theorem for the Wiener algebras $W$ and ${W^ + }$ of absolutely convergent Fourier and Taylor series respectively, also the disc algebra $A(\overline D )$ and the subalgebras ${A^n}(\overline D )$ of functions whose $n$th derivatives extend continuously to $\overline D = \{ z:\left | z \right | \leqslant 1\}$.

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