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Journal of Convex Analysis 14 (2007), No. 4, 729--766
Copyright Heldermann Verlag 2007

Balanced Complex Polytopes and Related Vector and Matrix Norms

Nicola Guglielmi
Dipartimento di Matematica, UniversitÓ di L'Aquila, Via Vetoio -- loc. Coppito, 67100 l'Aquila, Italy

Marino Zennaro
Dip. di Matematica e Informatica, UniversitÓ di Trieste, Via A. Valerio 12/1, 34100 Trieste, Italy

We study the notion of balanced complex polytope as a generalization of a symmetric real polytope to the complex space Cn. We pay particular attention to the geometric properties of such complex polytopes and of their counterparts in the adjoint form. In particular, we stress the differences occurring with respect to the well-known real case. We also introduce and discuss the related definitions of complex polytope norm and adjoint complex polytope norm.

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