Buch, Englisch, Band 14, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2409 g
Buch, Englisch, Band 14, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2409 g
Reihe: SpringerBriefs in Mathematical Physics
ISBN: 978-3-319-47701-5
Verlag: Springer International Publishing
This elementary account of the Kadison-Singer conjecture is very well-suited for graduate students interested in operator algebras and states, researchers who are non-specialists of the field, and/or interested in fundamental quantum physics.
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Weitere Infos & Material
Introduction.-Pure state extensions in linear algebra.- Density operators and pure states.- Extensions of pure states.- State spaces and the Kadison-Singer property.- States on C*-algebras.- Pure states and characters.- Extensions of pure states.- Properties of extensions and restrictions.- Maximal abelian C*-subalgebras.- Maximal abelian C*-subalgebras.- Examples of maximal abelian C*-subalgebras.- Minimal projections in maximal abelian von Neumann algebras.- Unitary equivalence.- Minimal projections.- Subalgebras without minimal projections.- Subalgebras with minimal projections.- Classification.- Stone-Cech compactification.- Stone-Cech compactification.- Ultrafilters.- Zero-sets.- Ultra-topology.-Convergence of ultrafilters for Tychonoff spaces.- Pushforward.- Convergence of ultrafilters for compact Hausdorff spaces.- Universal property.- The continuous subalgebra and the Kadison-Singer conjecture.- Total sets of states.- Haar states.- Projections in the continuous subalgebra.- TheAnderson operator.- The Kadison-Singer conjecture.- The Kadison-Singer problem.- Real stable polynomials.- Realizations of random matrices.- Orthants and absence of zeroes.- Weaver’s theorem.- Paving theorems.- Proof of the Kadison-Singer conjecture.- Preliminaries.- Linear algebra.- Order theory.- Topology.- Complex analysis.- Functional Analysis and Operator Algebras.- Basic functional analysis.- Hilbert spaces.- C*-algebras.- Von Neumann algebras.- Additional material.- Transitivity theorem.- G-sets, M-sets and L-sets.- GNS-representation.- Miscellaneous.- Notes and remarks.- References.