All Questions

Let $H$ be a Hilbert space, and let $A$ be a contraction (bounded linear operator of norm $\leq 1$) on $H$. I heard in a recent talk that there is a (apparently famous) result due to Sz-Nagy which ...

Let $H$ be a Hilbert space and $T: H \to H$ be a contraction. In Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes, von Neumann proved the inequality $$ \lVert p(T)\rVert \leq \sup \...

Let $A$ and $B$ be two matrices of eigenvalues $\lambda_i$ and $\mu_i$, respectively. The spectral variation of $B$ w.r.t. $A$ and the eigenvalue variation of $B$ and $A$ are, respectively, \begin{...

We define an increasing sequence of closed subspaces \begin{align*} V_{0} \subset V_{1} \subset V_{\ell} \subset \dots \end{align*} of $L^2(I)$ where $I=(0,x_{max})$, and each $V_{\ell}$ is equipped ...

I'm looking for an appropriate measure to quantify the extent to which two matrices commute. In other words, if A and B are two n×n Hermitian matrices, and [A,B]=C. I'd like a function μ:Cn×n→[0,∞) ...

I'm looking for a reference on linear, bounded, self-adjoint operators defined on the product space, $T:E\times F\to E\times F$ such that $$Tx = \begin{pmatrix}A & B \\ C & D \end{pmatrix}\...