Noncommutative Analysis, Operator Theory and Applications (Operator Theory: Advances and Applications (252))

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. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek. Front Matter....Pages i-vii Pimsner Algebras and Circle Bundles....Pages 1-25 A Fractional Dirac Operator....Pages 27-41 On the Sylvester Equation over Quaternions....Pages 43-75 The Essential Centre of the mod a Diagonalization Ideal Commutant of an n-tuple of Commuting Hermitian Operators....Pages 77-80 Clifford–Hermite Polynomials in Fractional Clifford Analysis....Pages 81-95 Negative Definite Functions on Groups with Polynomial Growth....Pages 97-104 An Introduction to Superoscillatory Sequences....Pages 105-121 Restriction and Factorization for Isometric and Symmetric Operators in Almost Pontryagin Spaces....Pages 123-170 Measurements vs. Interactions: Tracks in a Wilson Cloud Chamber....Pages 171-180 The Radii Problems for Holomorphic Mappings in J*-algebras....Pages 181-192 Lévy Processes on Quantum Permutation Groups....Pages 193-259 New Results on Old Spectral Triples for Fractals....Pages 261-270 Why Are Orlicz Spaces Useful for Statistical Physics?....Pages 271-283