Added a handful of examples.
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Bokuan Li
2026-06-02 21:39:59 -04:00
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\section{$B(H)$}
\label{section:hilbert-endomorphism}
\begin{definition}[$B(H)$]
\label{definition:hilbert-endomorphism}
Let $H$ be a Hilbert space, then $B(H) = L(H; H)$ is the algebra of all bounded linear operators on $H$.
\end{definition}
% 1. Every non-trivial ideal of B(H) contains the finite-rank operators.
% 2. If H is separable, then the only non-trivial closed idela of B(H) are the compact operators.