Year: 2017
Type: preprint
Abstract: For a completely regular space $X$ and a non-vanishing self-adjoint closed subalgebra $H$ of $C_B(X)$ which separates points from closed sets in $X$ we construct the Gelfand spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of the compactification of $X$ generated by $H$. The simple construction of $\mathfrak{sp}(H)$ enables easier examination of its properties. We illustrate this by an example showing that the space $\mathfrak{sp}(H)$ is separable metrizable if and only if $H$ is countably generated.
Source: arXiv (Cornell University)
Authors: Farhadi, M., Koushesh, M. R.
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2782210455