Difference between revisions
kadison-singer
Status and infobox
- status:
—→ solved - tier:
—→ V3 - kind:
—→ problem - year:
—→ 1959 - statement:
—→ Does every pure state on the diagonal of B(ℓ²) extend uniquely to a pure state on all of B(ℓ²)?
Source +21 −0
+---
+title: Kadison–Singer problem
+kind: problem
+status: solved
+tier: V3
+year: 1959
+authors: Richard Kadison and Isadore Singer
+statement: Does every pure state on the diagonal of B(ℓ²) extend uniquely to a pure state on all of B(ℓ²)?
+space: analysis
+---
+It started as a question about the foundations of quantum mechanics and was shown equivalent to problems in a dozen fields. The solution came from graph theory, through interlacing polynomials, the same method the authors used to build Ramanujan graphs. A question in operator algebras was settled by a combinatorial method.
+
+*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*
+
+Posed 1959, Richard Kadison and Isadore Singer. Closed 2013, Adam Marcus, Daniel Spielman and Nikhil Srivastava.
+
+## Sources
+
+- [Wikipedia: Kadison–Singer problem](https://en.wikipedia.org/wiki/Kadison%E2%80%93Singer_problem)
+
+[[Space:analysis|Analysis and PDE]] · [[Continent:mathematics|Mathematics]]
Revision 43 as rendered
It started as a question about the foundations of quantum mechanics and was shown equivalent to problems in a dozen fields. The solution came from graph theory, through interlacing polynomials, the same method the authors used to build Ramanujan graphs. A question in operator algebras was settled by a combinatorial method.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 1959, Richard Kadison and Isadore Singer. Closed 2013, Adam Marcus, Daniel Spielman and Nikhil Srivastava.