Global minimum and orthogonality in C p ‐classes

In this paper we use recent results [14] to establish various characterizations of the global minimum of the map F ψ : U → ℝ + defined by F ψ ( X ) = ‖ ψ ( X )‖ p (1 < p < ∞) where ψ : U → C p is a map defined by ψ ( X ) = S + ϕ ( X ), with ϕ : B ( H ) → B ( H ) a linear map and S ∈ C p , and U = { X ∈ B ( H ): ϕ ( X ) ∈ C p }. Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)