The eighteenth International Workshop on Operator Theory and Applications (IWOTA) was hosted by the Unit for Business Mathematics and Informatics of the North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference was dedicated to Professor Joseph A. Ball on the occasion of his 60th birthday and to Professor Marinus M. Kaashoek on the occasion of his 70th birthday, and we wish to similarly honour them by dedicating this volume of the proceedings to them. TheaimoftheIWOTAmeetingsistobringtogethermathematiciansworking in operator theory and its applications to related ?elds. Each conference therefore has a unique character, depending on the related ?elds chosen by the local or- nizers. In the present case Functional Analysis and Von Neumann algebras were decided on, due to the number of people actively working in those ?elds in South Africa. The meetings are intended to be truly international (the seventeen pre- ous ones were held in 11 di?erent countries) and this conference was no exception, with participants drawn from 17 countries. IWOTA is directed by an international steering committee of 25 members under the guidance of the president I. Gohberg (Tel Aviv), assisted by the Vice PresidentsJ.W.Helton(LaJolla)andM.A.Kaashoek(Amsterdam).TheProce- ings of the IWOTA workshops regularly appear in the Birkhauser series: Operator Theory: Advances and Applications, and we thank them for their willingness to continue this cooperation by publishing this volume.

Zusammenfassung
This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.

Inhalt
Multivariable Operator-valued Nevanlinna-Pick Interpolation: a Survey.- On the Unit Ball of Operator-valued H 2-functions.- On an Interpolation Problem for Generalized Schur Functions.- The Algebra of ?-measurable Operators.- Holomorphic and Bergman-type Spaces.- A Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting.- Nowhere Density of the Set of Non-norm-attaining Functionals.- A Stochastic Double Product in Non-Fock Quantum Stochastic Calculus.- Singular Integral Operators on Variable Lebesgue Spaces with Radial Oscillating Weights.- Reverse Martingales in Riesz Spaces.- Contractivity of the H ?-calculus and Blaschke Products.- Invertibility in the Algebra of ?-measurable Operators.- Analyticity of Semigroups Related to a Class of Block Operator Matrices.- Derivations of ?-measurable Operators.- On Hyperinvariant Subspaces for Linear Maps of Real Vector Spaces.