The Lidskii trace property and the nest approximation property in Banach spaces
Overview
Research
Identity
Additional Document Info
Other
View All
Overview
abstract
2016 Elsevier Inc. For a Banach space X, the Lidskii trace property is equivalent to the nest approximation property; that is, for every nuclear operator on X that has summable eigenvalues, the trace of the operator is equal to the sum of the eigenvalues if and only if for every nest N of closed subspaces of X, there is a net of finite rank operators on X, each of which leaves invariant all subspaces in N, that converges uniformly to the identity on compact subsets of X. The Volterra nest in L p (0,1), 1p<, is shown to have the Lidskii trace property. A simpler duality argument gives an easy proof of the result [2, Theorem 3.1] that an atomic Boolean subspace lattice that has only two atoms must have the strong rank one density property.
