Harte, Robin E.2024-07-122024-07-122019Harte, R. E. (2019). Gelfand's theorem unplugged. International Conference of Mathematical Sciences . s. 020002-(1)-020002-(4).978-0-7354-1816-5https://aip.scitation.org/toc/apc/2086/1?windowStart=50&size=50https://hdl.handle.net/20.500.12415/2749It was Norbert Wiener who made the observation that if a non-vanishing continuous function on the circle has anabsolutely convergent Fourier series, then so does its reciprocal. Israel Gelfand saw in this picture the concept of a commutativeBanach algebra, and extended Wiener’s observation to these Banach algebra elements, with a completely di?erent proof based on“maximal ideals”. In this note we claim that the several variable spectral mapping theorem is able to unplug the Gelfand theoryfrom the life support system of these elusive maximal ideals.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessArticle020002-4020002-1