Memoirs of the American mathematical society; vol.205, N 964 (Providence, 2009). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаPopescu G. Operator theory on noncommutative domains. - Providence: American Mathematical Society, 2009. - vi, 124 p. - (Memoirs of the American mathematical society; vol.205, N 964). - Bibliogr.: p.121-124. - ISBN 978-0-8218-4710-7; ISSN 0065-9266
 

Место хранения: 013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents
 
Introduction .................................................... 1

Chapter 1. Operator algebras associated with noncommutative
           domains .............................................. 9

1.1. The noncommutative domain fig.2ƒ and a universal model ......... 9
1.2. The domain algebra fig.3n(fig.2ƒ) and its representations ......... 17
1.3. The Hardy algebra Fn(fig.2ƒ) .................................. 22
1.4. Functional calculus for n-tuples of operators in fig.2ƒ ....... 26
1.5. The noncommutative variety fig.4ƒj and a functional 
     calculus .................................................. 32
1.6. Weighted shifts, symmetric weighted Fock spaces, and
     multipliers ............................................... 35

Chapter 2. Free holomorphic functions on noncommutative
           domains ............................................. 45

2.1. Free holomorphic functions and Poisson transforms ......... 45
2.2. Schwarz lemma and Bohr's inequality for Fn(fig.2ƒ) ............ 51
2.3. Weierstrass and Montel theorems for the algebra Hol(fig.2ƒ) ... 56
2.4. Cauchy transforms and analytic functional calculus for
     n-tuples of operators ..................................... 59

Chapter 3. Model theory and unitary invariants on 
           noncommutative domains .............................. 71

3.1. Weighted shifts and invariant subspaces ................... 71
3.2. C*-algebras associated with noncommutative varieties
     and Wold decompositions ................................... 76
3.3. Dilations on noncommutative domains and varieties ......... 82
3.4. Characteristic functions and model theory ................. 92
3.5. Curvature invariant for n-tuples of operators in fig.2p ...... 104

Chapter 4. Commutant lifting and applications ................. 111

4.1. Interpolation on noncommutative domains .................. 111
4.2. Corona theorem for a class of Hardy algebras ............. 117
4.1. Bibliography ............................................. 121


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