COMPLETELY BOUNDED MAPS AND OPERATOR ALGEBRAS

By O. FANAS

CONTENTS INTRODUCTION POSITIVE MAPS COMPLETELY POSITIVE MAPS DILATION THEOREMS COMMUTING CONTRACTIONS ON HILBERT SPACE COMPLETELY POSITIVE MAPS INTO MN ARVESON’S EXTENSION THEOREMS COMPLETELY BOUNDED MAPS COMPLETELY BOUNDED HOMOMORPHISMS POLYNOMIALLY BOUNDED AND POWER-BOUNDED OPERATORS APPLICATIONS TO K-SPECTRAL SETS TENSOR PRODUCTS AND JOINT SPECTRAL SETS ABSTRACT CHARACTERIZATIONS OF OPERATOR SYSTEMS AND OPERATOR SPACES AN OPERATOR SPACE BESTIARY INJECTIVE ENVELOPES ABSTRACT OPERATOR ALGEBRAS COMPLETELY BOUNDED MULTILINEAR MAPS AND THE HAAGERUP TENSOR NORM UNIVERSAL OPERATOR ALGEBRAS AND FACTORIZATION SIMILARITY AND FACTORIZATION