The Kadison-Singer property. (2016)

• Record Type: Book
• Further Information: Note: Marco Stevens.
• Authors: Stevens, Marco
• Contents: 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-Čech compactification.- Stone-Čech 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.- The Anderson 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.
• Publisher Details: Cham : Springer
• Publication Date: 2016
• Copyright Date: 2016
• Extent: 1 online resource (140 pages)
• Subjects: 515.733; Mathematics; Hilbert space; Algebra; Mathematics -- Functional Analysis; Science -- Mathematical Physics; Functional analysis & transforms; Mathematical physics; Operator theory; Mathematical physics; Functional analysis
• Languages: English
• ISBNs: 9783319477022
• Related ISBNs: 9783319477015
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.