Dissertationes mathematicae. Vol.465: Componentwise and Cartesian decompositions of linear relations / Hassi S., de Snoo H.S.V., Szafraniec F.H. - Warszawa: Institute of mathematics, Polish academy of sciences, 2009. - 58 p. - Ref.: p.56-58. - Ind.: p.59. - ISSN 0012-3862  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

1 Introduction ................................................. 5 1.1 Some background ......................................... 5 1.2 Decomposition of relations .............................. 7 1.3 Brief description ....................................... 9 2 Preliminaries ................................................ 9 2.1 Linear relations in a Hilbert space ..................... 9 2.2 Adjoint relations ...................................... 11 2.3 Special relations ...................................... 12 2.4 Sums and products ...................................... 12 2.5 Some auxiliary results ................................. 15 2.6 Points of regular type and the resolvent set ........... 17 2.7 Defect numbers ......................................... 18 2.8 The numerical range .................................... 19 2.9 An extension preserving the numerical range ............ 20 2.10 Formally domain tight and domain tight relations ....... 21 2.11 Selfadjointness of symmetric relations ................. 24 2.12 Extensions in larger Hilbert spaces .................... 24 2.13 Range tight relations .................................. 25 2.14 Maximality with respect to the numerical range ......... 26 3 Componentwise decompositions of relations ................... 27 3.1 Canonical decompositions of relations .................. 27 3.2 Componentwise decompositions of relations via the operator part ...................................... 31 3.3 Componentwise decompositions for relations via the multivalued part ................................... 36 3.4 Componentwise decompositions of adjoint relations ...... 39 3.5 Some examples of operators or relations which are not decomposable ........................................... 39 4 Orthogonal componentwise decompositions of relations ........ 43 4.1 Orthogonality for componentwise sum decompositions of relations .............................................. 43 4.2 Orthogonality for componentwise sum decompositions of adjoint relations ...................................... 45 4.3 Some classes of relations with orthogonal componentwise decompositions ........................... 48 5 Cartesian decompositions of relations ....................... 49 5.1 Real and imaginary parts of relations .................. 50 5.2 Cartesian decompositions of relations .................. 53 References ..................................................... 56 Index .......................................................... 59