Cho-Ho Chu

Harmonic functions on groups and Fourier algebras

1. Introduction.- 2. Harmonic functions on locally compact groups: 2.1. Preliminaries and notation. 2.2. Poisson representation of harmonic functions. 2.3. Semigroup structures of the Poisson space. 2.4. Almost periodic harmonic functions. 2.5. Distal harmonic functions. 2.6. Transitive group actions on Poisson spaces. 2.7. Examples.- 3. Harmonic functionals on Fourier algebras: 3.1. Fourier algebras. 3.2. Harmonic functionals and associated ideals. 3.3. Jordan structures of harmonic functionals. 3.4. Classification of harmonic functionals.- References.- List of symbols.- Index.

The Dunford–Pettis property in Jb*-Triples

JB*-triples occur in the study of bounded symmetric domains in several complex variables and in the study of contractive projections on C*-algebras. These spaces are equipped with a ternary product {·,·,·}, the Jordan triple product , and are essentially geometric objects in that the linear isometries between them are exactly the linear bijections preserving the Jordan triple product (cf. [ 23 ]).

The convolution equation of Choquet and Deny on nilpotent groups

G. Choquet and J. Deny have characterized the positive solutions μ of the convolution equation σ*μ=μ of measures on locally compact abelian groups, for a given positive measure σ. By elementary methods, we extend their characterization to locally compact nilpotent groups which complements the various existing results on the equation, and we work out the solutions μ explicitly for the Heisenberg groups and some nilpotent matrix groups, by finding all the exponential functions on these groups.

Hypercyclicity of weighted convolution operators on homogeneous spaces

Let 1 ≤ p < oo. We show that a weighted translation operator on the L P space of a homogeneous space is hypercyclic under some condition on the weight. This condition is also necessary in the discrete case and is equivalent to hereditary hypercyclicity of the operator. The condition can be strengthened to characterise topologically mixing weighted translation operators on discrete spaces.

Matrix convolution operators on groups

Lebesgue Spaces of Matrix Functions.- Matrix Convolution Operators.- Convolution Semigroups.

The convolution equation of Choquet and Deny on [IN]-groups

Let σ be a probability measure on a locally compact groupG. A real Borel functionf onG is called σ-harmonic if it satisfies the convolution equation σ*f=f. Given that σ isnonsingular with its translates, we show that the bounded σ-harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If σ is nondegenerate and absolutely continuous, we solve the more general equation σ*μ=μ for positive measure μ on those groups which are metrizable and separable.

Real contractive projections on commutative C\(^*\)-algebras

Complex (Banach) Jordan triples occurred in the study of bounded symmetric domains in several complex variables and in the study of contractive projections on (complex) C∗-algebras. These spaces are equipped with a ternary product, the Jordan triple product, and are essentially geometric objects in that the linear isometries between them are exactly the linear maps preserving the triple product [13].

Separably injective C*-algebras

We show that a C*-algebra is a 1-separably injective Banach space if and only if it is linearly isometric to the Banach space

Jordan Structures in Bounded Symmetric Domains

{C_0(\Omega)}