Added basic facts about the Gelfand transform.

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Bokuan Li
2026-06-03 15:44:13 -04:00
parent 56f3ae37f7
commit f72f815c72
6 changed files with 135 additions and 1 deletions

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@@ -13,8 +13,12 @@
$[x]_{sp}$ & The spectral radius of $x$. & \autoref{definition:spectral-radius} \\
$\Omega(A)$ & Space of multiplicative functionals on $A$. & \autoref{definition:multiplicative-functional} \\
$\cm(A)$ & Maximal ideal space of $A$. & \autoref{definition:maximal-ideal} \\
$\Gamma = \Gamma_A$ & The Gelfand transform on $A$. & \autoref{definition:gelfand-transform} \\
$M_n(\complex)$ & Algebra of $n \times n$ matrices over $\complex$. & \autoref{definition:matrix-algebra} \\
$B(H)$ & Algebra of bounded operators on a Hilbert space. & \autoref{definition:hilbert-endomorphism} \\
$A(D)$ & The disk algebra. & \autoref{definition:disk-algebra} \\
$H^\infty(D)$ & The Hardy space. & \autoref{definition:hardy-space} \\
$\ell^1(\integer)$ & Convolution algebra on $\integer$. &\autoref{definition:convolution-algebra-integer} \\
$\delta_0$ & Multiplicative unit of $\ell^1(\integer)$. & \autoref{definition:convolution-algebra-integer} \\
\end{tabular}