info:eu-repo/semantics/article
Best approximation by diagonal operators in Schatten ideals
Fecha
2021-07Registro en:
Bottazzi, Tamara Paula; Best approximation by diagonal operators in Schatten ideals; Elsevier Science Inc.; Linear Algebra and its Applications; 620; 7-2021; 1-26
0024-3795
CONICET Digital
CONICET
Autor
Bottazzi, Tamara Paula
Resumen
If X is the set of compact or p-Schatten operators over a complex Hilbert separable space H, we study the existence and characterization properties of Hermitian A∈X such that |||A|||≤|||A+D|||,for allD∈D(X) or equivalently |||A|||=minD∈D(X)|||A+D|||=dist(A,D(X)), where D(X) is the subspace of diagonal operators of X in any prefixed basis of H and |||⋅||| is the usual operator norm in each X. We use Birkhoff-James orthogonality as a tool to characterize and develop properties of these operators in each context. We also provide several illustrative examples.