The “Up-Down” Problem For Operator Algebras
AUTOR(ES)
Pedersen, Gert K.
RESUMO
It is shown that for any C*-algebra A of operators on a separable Hilbert space, there is, for each self-adjoint operator x in the strong closure of A, a sequence {xn} of self-adjoint operators, each of which is the strong limit of a monotone increasing sequence of self-adjoint operators from A, such that {xn} is monotone decreasing and strongly convergent to x.
