Davidson K.R. Operator algebras for multivariable dynamics / K.R.Davidson, E.G.Katsoulis. - Providence: American Mathematical Society, 2011. - vii, 53 p. - (Memoirs of the American Mathematical Society; Vol.209, N 982). - Bibliogr.: p.51-53. - ISBN 978-0-8218-5302-3; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Chapter 1. Introduction ......................................... 1 1.1. The one variable ease ...................................... 3 1.2. Universal operator algebras................................. 4 Chapter 2. Dilation Theory ...................................... 7 2.1. Dilation for the tensor algebra ............................ 7 2.2. Boundary representations and the C*-envelope ............... 9 2.3. С*-correspondences ........................................ 13 2.4. Dilation and the semi-crossed product ..................... 17 Chapter 3. Recovering the Dynamics ............................. 23 3.1. Fourier series and automatic continuity ................... 23 3.2. Characters and nest representations ....................... 26 3.3. Piecewise conjugate multisystems .......................... 30 3.4. The main theorem .......................................... 32 3.5. The converse .............................................. 35 Chapter 4. Semisimplicity ...................................... 43 4.1. Wandering sets and recursion .............................. 43 4.2. Semisimplicity ............................................ 44 Chapter 5. Open Problems and Future Directions ................. 49 Bibliography ................................................... 51