Kadison–Singer problemMatrix algebrasOperator algebrasPrimary 46LM× matrices and write for the direct sum of the n. So a typical element of has the form$$ x = x_1\\oplus x_2 \\cdots \\oplus x_n \\oplus \\cdots, $$where ${x_n \\in M_n}$ and ${\\|x\\| = \\sup...
The recent surprising solution to this problem by Marcus, Spielman and Srivastava was a significant achievement and a significant advance for all these areas of research. We will look at many of the known equivalent forms of the Kadison-Singer Problem and see what are the best new theorems ...
We show that the Kadison-Singer problem, asking whether the pure states of the diagonal subalgebra $ell^infty-Bbb Nsubset -Cal B(ell^2-Bbb N)$ have unique state extensions to $-Cal B(ell^2-Bbb N)$, is equivalent to a similar statement in II$_1$ factor framework, concerning the ...
original results. Survey articles should not be submitted. The relationship to the Kadison-Singer Problem can be close, e.g. extension of the methods of the solution or a substantially
We show that the Kadison–Singer problem, asking whether the pure states of the diagonal subalgebra \\({\\ell^\\infty\\mathbb{N}\\subset \\mathcal{B}(\\ell^2\\mathbb{N})}\\) have unique state extensions to \\({\\mathcal{B}(\\ell^2\\mathbb{N})}\\) , is equivalent to a...
The Kadison-Singer Problem and the Uncertainty Principle Eric Weber joint with Pete CasazzaWeber, Eric
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 ...
In the details below, the following concepts and terms will play an important role; (for reference, see also Appendix F): The Stone-ech compactification, states, normal, non-normal, extensions, pure states, uniqueness of pure-state extensions....
N. Weaver. The Kadison-Singer problem in discrepancy theory. Discrete Mathematics, 278:227- 239, 2004.N. Weaver. The Kadison-Singer problem in discrepancy theory. ArXiv Mathematics e-prints, September 2002.Weaver, N.: The Kadison–Singer problem in discrepancy theory. Discrete Math. 278 , ...
W. Lawton, Minimal sequences and the Kadison-Singer problem, Bul- letin of the Malaysian Mathematical Sciences Society, http://math. usm. my/bulletin,(2) 33 (2010), no. 2, 169-176.W. Lawton, Minimal sequences and the Kadison-Singer problem, Bull. Malays. Math. Sci. Soc. 33 (2010...