Operator Algebras, Operator Theory and Applications

This book is composed of three survey lecture courses and nineteen invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory.

The lecture courses are:

Subalgebras of Graph C*-algebras, by Stephen Power: An introduction to two classes of non-selfadjoint operator algebras, the generalized analytic Toeplitz algebras associated with the Fock space of a graph and subalgebras of graph C*-algebras;

C*-algebras and asymptotic spectral theory, by Bernd Silbermann: Three topics on numerical functional analysis that are the cornerstones in asymptotic spectral theory: stability, fractality and Fredholmness;

Toeplitz operator algebras and complex analysis, by Harald Upmeier: A survey concerning Hilbert spaces of holomorphic functions on Hermitian symmetric domains of arbitrary rank and dimension, in relation to operator theory, harmonic analysis and quantization.

Summer School Lecture Notes.- Subalgebras of Graph C*-algebras.- C*-algebras and Asymptotic Spectral Theory.- Toeplitz Operator Algebras and Complex Analysis.- Workshop Contributed Articles.- Rotation Algebras and Continued Fractions.- On the Fredholm Index of Matrix Wiener-Hopf plus/minus Hankel Operators with Semi-almost Periodic Symbols.- Diffraction by a Strip and by a Half-plane with Variable Face Impedances.- Factorization Algorithm for Some Special Matrix Functions.- On a Radon Transform.- Extensions of ?-C* -algebras.- Higher-order Asymptotic Formulas for Toeplitz Matrices with Symbols in Generalized Hölder Spaces.- Nonlocal Singular Integral Operators with Slowly Oscillating Data.- Poly-Bergman Projections and Orthogonal Decompositions of L 2-spaces Over Bounded Domains.- Vekua’s Generalized Singular Integral on Carleson Curves in Weighted Variable Lebesgue Spaces.- On Homotopical Non-invertibility of C*-extensions.- Galois-fixed Points and K-theory for GL(n).- Spectral Factorization, Unstable Canonical Factorization, and Open Factorization Problems in Control Theory.- Compact Linear Operators Between Probabilistic Normed Spaces.- Essential Spectra of Pseudodifferential Operators and Exponential Decay of Their Solutions. Applications to Schrödinger Operators.- On Finite Sections of Band-dominated Operators.- Characterization of the Range of One-dimensional Fractional Integration in the Space with Variable Exponent.- Orbit Representations and Circle Maps.- On Generalized Spherical Fractional Integration Operators in Weighted Generalized Hölder Spaces on the Unit Sphere.