On symmetricity of orthogonality with respect to numerical radius norm
Shamim Sohel
Abstract
We study Birkhoff-James orthogonality and local symmetric points in the space C(K,X) of vector-valued continuous functions equipped with a numerical-radius type (semi-)norm. We extend the theory of abstract numerical ranges to semi-normed spaces and obtain complete characterizations of the left and right symmetric points of C(K,X) with respect to the numerical-radius (semi-) norm. We also establish corresponding results for the space K(X) of compact operators on X.
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