Abstract

We study the notion of balanced complex polytope as a generalization of a symmetric real polytope to the complex space Cn\mathbb{C}^n. 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

Author information

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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

References

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Suggested citation

N. Guglielmi, M. Zennaro. “Balanced Complex Polytopes and Related Vector and Matrix Norms.” Journal of Convex Analysis 14 (2007), No. 4, 729–766. https://doi.org/10.68381/jca14043

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.