Diagonal Ranks of Semigroups

Decomposition and Classification of Generic Quantum Markov Semigroups: The Gaussian Gauge Invariant Case

Abstract We study a class of generic quantum Markov semigroups on the algebra of all bounded operators on a Hilbert space h arising from the stochastic limit of a discrete system with generic Hamiltonian HS , acting on h, interacting with a Gaussian, gauge invariant, reservoir. The self-adjoint operator HS determines a privileged orthonormal basis of h. These semigroups leave invariant diagonal...

Weighted Norm Inequalities, Off-diagonal Estimates and Elliptic Operators Part Ii: Off-diagonal Estimates on Spaces of Homogeneous Type Pascal Auscher and José

This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant L − L estimates. We propose a definition in spa...

Asymptotics of Semigroups Generated by Operator Matrices

We survey some known results about generator property of operator matrices with diagonal or coupled domain. Further, we use basic properties of the convolution of operator-valued mappings in order to obtain stability results for such semigroups. 1. Operator matrices with diagonal domain While tackling abstract problems that are related to concrete initial–boundary value problems with dynamical ...

The Ranks of Some Transformation Semigroups on a Finite Set

Part Ii: Off-diagonal Estimates on Spaces of Homogeneous Type Pascal Auscher and José María Martell

This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant L − L estimates. We propose a definition in spa...