Noncommutative Analysis, Operator Theory and Applications

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications.

Preface.- Pimsner algebras and noncommutative circle bundles.- A fractional Dirac operator.- On the Sylvester equation over quaternions.- The Essential Centre of the mod a Diagonalization Ideal Commutant of an n-tuple of Commuting Hermitian Operators.- Clifford-Hermite polynomials in fractional Clifford analysis.- Negative definite functions on groups with polynomial growth.- An introduction to superoscillatory sequences.- Restriction and factorization for isometric and symmetric operators in almost Pontryagin spaces.- Measurements vs Interactions: tracks in a Wilson cloud chamber.- The radii problems for holomorphic mappings in J*-algebras.- Lévy Processes on Quantum Permutation Groups.- New results on old spectral triples for fractals.- Why are Orlicz spaces useful for Statistical Physics?.