We study tent spaces on general measure spaces (Ω, μ). We assume that there exists a semigroup of positive operators on Lp(Ω, μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman’s H1-BMO du...

Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator B defined on an infinite-dimensional Hilbert space U is an admissible control operator if for every element u ∈ U the vector Bu defines an admissible control operator. The other conjecture says that B is an admissible control operator if a certain resolvent estimate ...

We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary evolution equations driven by a large class of differential pseudo-differential operators L, both finite infinite dimension. The assumptions are given terms the semigroup generated L. cover cases fractional Laplacians Ornstein-Uhlenbeck with diffusion dimension, several types local nonlocal operators, as we...

In this paper, varieties of completely regular semigroups are studied. This paper is divided into six sections. Section 1 contains an introduction to varieties of completely regular semigroups and preliminaries. Most of the notation needed in this paper is given. In Section 2, the operators ←− ( ) and −→ ( ) on the lattice of subvarieties of varieties of completely regular semigroups are invest...

Introduction. The question of ergodicity of a semigroup of bounded linear operators on a Banach space has been reduced, by Alaoglu and Birkhoff [l],1 Day [2, 3], and Eberlein [4], to the study firstly of the ergodicity of the semigroup itself and secondly, of the ergodicity of each element of the Banach space with respect to this ergodic semigroup. In the case of a bounded and commutative semig...

Introduction. In § I, it is shown that M(G)*, the space of bounded linear functionals on M(G), can be represented as a semigroup of bounded operators on M(G). Let A denote the non-zero multiplicative linear functionals on M(G) and let P be the norm closed linear span of A in M(G)*. In § II, it is shown that P , with the Arens multiplication, is a commutative J3*-algebra with identity. Thus P = ...

ABSTRACT. The key result in the paper concerns two transformations, Φ : (ρ, ψ) 7→ φ and Bt : ψ 7→ φ, where ρ, ψ, φ are states on the algebra of non-commutative polynomials, or equivalently joint distributions of d-tuples of non-commuting operators. These transformations are related to free probability: if ⊞ is the free convolution operation, and {ρt} is a free convolution semigroup, we show tha...

The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multidimensional Euclidean space; in case that it ...

Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: (i) for many simple C∗-algebras, the Thomsen semigroup is recovered functorially from the Elliott invariant, and this yields a new proof of Elliott’s classification theorem for simple, unital AI algebras; (ii) for the algebras in (i), classification of their Hilbert modules is similar to the von Neu...