Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

We discuss various aspects of positive kernel method quantization the one-parameter groups $\tau_t \in \mbox{Aut}(P,\vartheta)$ automorphisms a $G$-principal bundle $P(G,\pi,M)$ with fixed connection form $\vartheta$ on its total space $P$. show that generator $\hat{F}$ unitary flow $U_t = e^{it \hat{F}}$ being $ is realized by generalized Kirillov-Kostant-Souriau operator whose domain consists...

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...