The Operator Theory conferences, organized by the Department of Mathematics of INCREST and the Department of Mathematics of the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operator theory. This book comprises carefully selected papers on theory of linear operators and related fields. Original results of new research in fast developing areas are included. Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are presented. The research contacts of the Department of :viathematics of INCREST with the National Committee for Science and Technology of Romania provided means for developing the research activity in mathematics; they represent the generous framework of these meetings too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for this exellent job.

Contenuti:

Foreword.- List of participants.- Programme of the conference.- Asymptotic properties for positive Toeplitz matrices and operators.- Multicyclic systems of commuting operators.- Regular J-inner matrix-functions and related continuation problems.- Spectral analysis for simply characteristic operators by Mourre’s method. I.- Noncommutative uniform algebras.- Operator theory in Krein spaces and operator pencils.- Extensions of groups and simple C*-algebras.- The Krein space (?H2)? and coefficients of analytic functions.- Completions and extensions.- Operator factorizations and quasi-similarity orbits.- Multiplication operators on Bergman spaces are reflexive.- Uniform boundness of the energy for time-periodic potentials.- Homology in Banach and polynormed algebras: some results and problems.- Large analytic functions.- Toeplitz operators on the Segal—Bargmann space of infinitely many variables.- A note on perturbations of selfadjoint operators in Krein spaces.- Projective representations of compact groups in C*-algebras.- On the general stable rank for pairs.- Wiener-Hopf operators on the positive semigroup of a Heisenberg group.- Derivations of certain nest-subalgebras of von Neumann algebras.- Boolean algebras of projections and spectral measures in dual spaces.- A vector extension of Loewner’s differential equation.- A RKHS on entire functions and its multiplication operator. An explicit example.- Joint spectral properties for pairs of permutable selfadjoint transformations.- Holomorphic functions taking their values in a quotient bornological space.- On causal nets of algebras.- On uniform dual algebras.

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