Questions tagged [hilbert-modules]
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$C(X)$-Fredholm operators and Atiyah-Jänich theorem
Let $X$ be a compact Hausdorff topological space and consider the Hilbert space $\ell^2(\mathbb N)$. As shown here, any $T\in C(X,\ell^2(\mathbb N))$ induces a $C(X)$-Fredholm operator
$$
\begin{array}...
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Strict topology on the multiplier algebra
Let $A$ be a $C^*$-algebra. Let $M(A)$ be its multiplier $C^*$-algebras. The strict topology on $M(A)$ is given by
$$x_\lambda \to x \iff \forall a\in A: (\|x_\lambda a-xa\| + \|ax_\lambda - ax\| \to ...