Anthony To-Ming Lau

Bio: Anthony To-Ming Lau is an academic researcher from University of Alberta. The author has contributed to research in topics: Locally compact group & Locally compact space. The author has an hindex of 33, co-authored 146 publications receiving 3611 citations. Previous affiliations of Anthony To-Ming Lau include Tokyo Institute of Technology & Australian National University.

The Second Duals of Beurling Algebras

Abstract: Introduction Definitions and preliminary results Repeated limit conditions Examples Introverted subspaces Banach algebras of operators Beurling algebras The second dual of $\ell^1(G,\omega)$ Algebras on discrete, Abelian groups Beurling algebras on $\mathbb{F}_2$ Topological centres of duals of introverted subspaces The second dual of $L^1(G,\omega)$ Derivations into second duals Open questions Bibliography Index Index of symbols.

Banach Algebras on Semigroups and on Their Compactifications

Abstract: Let $S$ be a (discrete) semigroup, and let $\ell^{\,1}(S)$ be the Banach algebra which is the semigroup algebra of $S$. The authors study the structure of this Banach algebra and of its second dual. The authors determine exactly when $\ell^{\,1}(S)$ is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are 'forbidden values' for this constant. Table of Contents: Introduction; Banach algebras and their second duals; Semigroups; Semigroup algebras; Stone-?ech compactifications; The semigroup $(\beta S, \Box)$; Second duals of semigroup algebras; Related spaces and compactifications; Amenability for semigroups; Amenability of semigroup algebras; Amenability and weak amenability for certain Banach algebras; Topological centres; Open problems; Bibliography; Index of terms; Index of symbols. (MEMO/205/966)

Topological centers of certain dual algebras

Abstract: Let A be a Banach algebra with a bounded approximate identity. Let Z1 and Z2 be, respectively, the topological centers of the algebras A** and (A*A)*. In this paper, for weakly sequentially complete Banach algebras, in particular for the group and Fourier algebras L1 (G) and A(G), we study the sets Z1, Z2, the relations between them and with several other subspaces of A** or A*.

On -amenability of Banach algebras

Abstract: Generalizing the notion of left amenability for so-called F-algebras [12], we study the concept of -amenability of a Banach algebra A, where is a homomorphism from A to . We establish several characterizations of -amenability as well as some hereditary properties. In addition, some illuminating examples are given.

Pseudospectra of linear operators

Abstract: If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ||An|| or ||exp(tA)||. More may be learned by examining the sets in the complex plane known as the pseudospectra of A, defined by level curves of the norm of the resolvent, ||(zI - A)-1||. Five years ago, the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications. Since that time, analogous computations have been carried out for differential and integral operators. This paper, a companion to the earlier one, presents ten examples, each chosen to illustrate one or more mathematical or physical principles.

Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups

Abstract: (A) In this paper we study some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Hausdorff) topological groups G on (Hausdorff) compact spaces X.

Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates

Abstract: Let $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy and BMO spaces associated to $L$, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that $L$ is a Schrodinger operator on $\mathbb{R}^n$ with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces $H^p_L(X)$ for $p>1$, which may or may not coincide with the space $L^p(X)$, and show that they interpolate with $H^1_L(X)$ spaces by the complex method.