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I was wondering if a version of the spectral theorem (the projection valued measure case) holds for linear pencils of the form $$ A-\lambda B $$ where $A,B$ are self-adjoint on some Hilbert space $\...

Kotani theory gives roughly that for ergodic operators there is a certain equivalence between absolutely continuous spectrum and an absolutely continuous density of states measure. I would like to ...

Definitions Representation Let $X \subset \mathbb{C}^N$ and $\mathcal{A}$ be an algebra in $\mathcal{C}(X)$. Also, we denote $L(H)$ as the set of all linear operators on HIlbert space $H$. We call $\...

[Repost from https://math.stackexchange.com/questions/4802593/generalization-of-borel-functional-calculus] Let $A$ be a normal operator on a Hilbert space $V$. The continuous functional calculus gives ...