Extending Multipliers from Semigroups

SEMIGROUPS OF WELL-BOUNDED OFERATORS AND MULTIPLIERS by

FUNCTIONAL CALCULUS AND SQUARE FUNCTIONS ON NONCOMMUTATIVE L p - SPACES

In this work we investigate semigroups of operators acting on noncommutative L-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, q-Ornstein-Uhlenbeck semigroups, and the noncommutative Poiss...

On a Class of Quasi-distribution Semigroups

A class of [r]-semigroups, extending the class of smooth distribution semigroups of Balabane and Emami-Rad, is introduced. Relations with integrated semigroups of Arendt are given as well as a generalization of deLaubenfels and Jazar’s result on relations between smooth semispectral distributions and integrated semigroups. AMS Mathematics Subject Classification (2000): 47D60,

Bmo Spaces Associated with Semigroups of Operators

We study BMO spaces associated with semigroup of operators on noncommutative function spaces (i.e. von Neumann algebras) and apply the results to boundedness of Fourier multipliers on non-abelian discrete groups. We prove an interpolation theorem for BMO spaces and prove the boundedness of a class of Fourier multipliers on noncommutative Lp spaces for all 1 < p < ∞, with optimal constants in p....

Onesided Inverses for Semigroups

In any semigroup S, we say that elements a and b are left inverses of each other if a = aba, b = bab and a L b, in which case we write a γ b. Right inverses are defined dually with the notation δ. Set τ = δγ. We study the classes of semigroups in which τ has some of the usual properties of a relation. We also consider properties of (maximal) completely simple subsemigroups of S. In terms of the...