Elias G. Katsoulis

Isomorphisms between topological conjugacy algebras

Abstract A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that is a continuous proper map on a locally compact Hausdorff space , for i= 1,2. We show that the dynamical systems and are conjugate if and only if some topological conjugacy algebra of is isomorphic as an algebra to some topological conjugacy algebra of . This implies as a corollary the complete classification of the semicrossed products , which was previously considered by Arveson and Josephson [W. Arveson, K. Josephson, Operator algebras and measure preserving automorphisms II, J. Funct. Anal. 4 (1969), 100–134.], Peters [J. Peters, Semicrossed products of C*-algebras, J. Funct. Anal. 59 (1984), 498–534.], Hadwin and Hoover [D. Hadwin, T. Hoover, Operator algebras and the conjugacy of transformations, J. Funct. Anal. 77 (1988), 112–122.] and Power [S. Power, Classification of analytic crossed product algebras, Bull. London Math. Soc. 24 (1992), 368–372.]. We also obtain a complete classification of all semicrossed products of the form , where denotes the disc algebra and a continuous map which is analytic on the interior. In this case, a surprising dichotomy appears in the classification scheme, which depends on the fixed point set of η. We also classify more general semicrossed products of uniform algebras.

Nest Representations of Directed Graph Algebras

This paper is a comprehensive study of the nest representations for the free semigroupoid algebra

Isomorphism invariants for multivariable C*-dynamics

{\mathfrak{L}}_G

Algebraic isomorphisms of limit algebras

of a countable directed graph

Interpolation problems for ideals in nest algebras

G

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

as well as its norm-closed counterpart, the tensor algebra

A non-selfadjoint Russo-Dye Theorem

{\mathcal{T}}^{+}(G)

Extreme points in triangular UHF algebras

. We prove that the finite-dimensional nest representations separate the points in

Operator Algebras and C*-correspondences: A Survey

{\mathfrak{L}}_G

Semicrossed products of the disk algebra

, and a fortiori, in