Journal of Operator Theory

Volume 60, Issue 2, Fall 2008 pp. 379-398.

Interpolation and balls in $\mathbb{C}^k$

Authors: Vern I. Paulsen (1) and James P. Solazzo (2)
Author institution: (1) Department of Mathematics, University of Houston, Houston, TX, 77204, U.S.A.
(2) Department of Mathematics, Coastal Carolina University, Conway, S.C., 29526 U.S.A.

Summary: We compare and classify various types of Banach algebra norms on $\CC^k$ through geometric properties of their unit balls. This study is motivated by various open problems in interpolation theory and in the isometric characterization of operator algebra norms.

Keywords: Interpolation bodies, k-idempotent operator algebras, Schur ideals.

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