All Questions

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 \...

Consider the following function $f: [-1,1] \rightarrow \mathbb{R}$, expanded in terms of Legendre functions, $$ f(y;\boldsymbol{\beta}) = \sum_{i=0}^{\infty} \beta_i P_i(y) $$ where $\boldsymbol{\beta}...

Let $X$ be a continuous linear self-adjoint operator on some Hilbert space $H$ and for arbitrary compact operators $A$ we have: $XA+AX=0.$ Does this imply that $X=0$ or can there be non-trivial ...