Maps Preserving Schattenp-Norms of Convex Combinations
Copyright policy )Maps Preserving Schattenp-Norms of Convex Combinations
We study mapsϕof positive operators of the Schattenp-classes (1<p<+∞), which preserve thep-norms of convex combinations, that is, ∥tρ+(1-t)σ∥p=∥tϕ(ρ)+(1-t)ϕ(σ)∥p, ∀ρ,σ∈𝒮p+(H)1, t∈[0,1]. They are exactly those carrying the formϕ(ρ)=UρU*for a unitary or antiunitaryU. In the casep=2, we have the same conclusion whenever it just holds∥ρ+σ∥2=∥ϕ(ρ)+ϕ(σ)∥2for all the positive Hilbert-Schmidt class operatorsρ,σof norm1. Some examples are demonstrated.
- National Sun Yat-sen University Taiwan
- Central China Normal University China (People's Republic of)
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), maps preserving Schatten \(p\)-norms, positive Hilbert-Schmidt class operators, QA1-939, Transformers, preservers (linear operators on spaces of linear operators), Mathematics
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), maps preserving Schatten \(p\)-norms, positive Hilbert-Schmidt class operators, QA1-939, Transformers, preservers (linear operators on spaces of linear operators), Mathematics
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