I'm interested in learning more about the duality between (locally compact) Hausdorff spaces and commutative $C^*$-algebras. Does anyone have an introductory textbook they recommend? My background in analysis consists of a year-long sequence in measure theory and complex analysis. I'm sure this duality comprises a part of most textbooks on functional analysis, so I'd be happy with any recommendations that introduce and discuss $C^*$-algebras. Thank you!
2026-04-02 12:42:18.1775133738
$C^*$-Algebras and Gelfand Duality Reference
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After some searching, I came across the textbook An Introduction to Noncommutative Geometry by Joseph Várilly. It contains a quick (and categorical) exposition of the Gelfand-Naimark theorem, along with a helpful table showing the dictionary between locally compact spaces and $C^*$-algebras.