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- W2950587932 abstract "Let $M_n$ denote the algebra of complex $ntimes n $ matrices and write $M$ for the direct sum of the $M_n$. So a typical element of $M$ has the form [x = x_1oplus x_2 ... oplus x_n oplus ...,] where $x_n in M_n$ and $|x| = sup_n|x_n|$. We set $D= {{x_n} in M: x_n$ is diagonal for all $N}$. We conjecture (contra Kadison and Singer (1959)) that every pure state of $D$ extends uniquely to a pure state of $M$. This is known for the normal pure states of D, and we show that this is true for a (weak*) open, dense subset of all the singular pure states of $D$. We also show that (assuming the Continuum hypothesis) $M$ has pure states that are not multiplicative on any maximal abelian *-subalgebra of $M$." @default.
- W2950587932 created "2019-06-27" @default.
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- W2950587932 date "2010-09-12" @default.
- W2950587932 modified "2023-09-27" @default.
- W2950587932 title "The Kadison-Singer problem for the direct sum of matrix algebras" @default.
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