It is shown that the direct integral decomposition of a non-self-adjoint operator algebra A has the diagonal A ∩ A* of this algebra as the algebra of diagonalizable operators if and only if almost all ...
We construct a pure state on the C*-algebra 𝓑(ℓ₂) of all bounded linear operators on ℓ₂, which is not diagonalizable [i.e., it is not of the form limu⩽T(ek), ek⩾ for any orthonormal basis (ek)kϵℕ of ...
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