Abstract
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.
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