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, Università di L'Aquila, Via Vetoio -- loc. Coppito, 67100 l'Aquila, Italy
guglielm@matematica.univaq.it
Marino Zennaro
Dip. di Matematica e Informatica, Università di Trieste, Via A. Valerio 12/1, 34100 Trieste, Italy
zennaro@univ.trieste.it
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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