5 problems

Let $X_1,\ldots,X_r$ be spectral operators in the sense of Dunford on separable Hilbert spaces $\mathcal{H}_1,\ldots,\mathcal{H}_r$. Assume there are positive self-adjoint operator…

Let $G$ be a Lie group of polynomial volume growth, generated by vector fields $X_1,\ldots,X_m$, and let $\slashed{D}_p$ be the $L^p$ realization of the Hodge–Dirac operator on … F…

Let $X$ be a $C^k$-manifold and $E$ a complex $C^k$ vector bundle of rank $r$ on $X$. Let $(y^1,\ldots,y^n)$ be a global coordinate system on $\Bbb R^n$, and let … be an assignment…

Let $H$ be a Hilbert space, let $L_1(H)$ denote the trace-class operators on $H$, and let $L_{1,cinfty}(H)$ denote the weak-$L_1$ space of compact operators $T$ whose singular valu…

Let $H$ and $A$ belong to a $C^{*}$-algebra, with $H$ a positive contraction satisfying $0\leq H\leq1$ and $\left\Vert A\right\Vert\leq1$. For the square-root function…