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The Kadison-Singer property

Author: Marco Stevens
Publisher: Cham, Switzerland : Springer, 2016.
Series: SpringerBriefs in mathematical physics, v. 14.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book gives a complete classification of all algebras with the Kadison-Singer property, when restricting to separable Hilbert spaces. The Kadison-Singer property deals with the following question: given a Hilbert space H and an abelian unital C*-subalgebra A of B(H), does every pure state on A extend uniquely to a pure state on B(H)? This question has deep connections to fundamental aspects of quantum physics,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Stevens, Marco.
Kadison-Singer property.
Cham, Switzerland : Springer, 2016
(OCoLC)958356212
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marco Stevens
ISBN: 9783319477022 3319477021
OCLC Number: 962437408
Description: 1 online resource.
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.
Series Title: SpringerBriefs in mathematical physics, v. 14.
Responsibility: Marco Stevens,

Abstract:

The Kadison-Singer property deals with the following question: given a Hilbert space H and an abelian unital C*-subalgebra A of B(H), does every pure state on A extend uniquely to a pure state on  Read more...

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