| Autor: |
Akemann, Charles A., Anderson, Joel, Tanbay, Betul |
| Rok vydání: |
2012 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
The Kadison-Singer Problem (K-S) has expanded since 1959 to a very large number of equivalent problems in various fields. In the present paper we will introduce the notion of weak paveability for positive elements of a von Neumann algebra M. This new formulation implies the traditional version of paveability iff K-S is affirmed. We show that the set of weakly paveable positive elements of $M^+$ is open and norm dense in $M^+$. Finally, we show that to affirm K-S it suffices to show that projections with compact diagonal are weakly paveable. Therefore weakly paveable matrices will either contain a counterexample, or else weak paveability must be an easier route to affirming K-S. |
| Databáze: |
arXiv |
| Externí odkaz: |
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