On complex strictly convex complexifications of Banach spaces

V. M. Kadets, A. Yu. Kellerman

V. N. Karazin Kharkiv National University

Abstract: We show that every real separable normed space may be complexified to a complex strictly convex normed space. The same result is obtained also for some classes of nonseparable spases, for example, for spases $X$ with 1-norming separable subspases in $X^*$; however, a space $\ell_\infty(\Gamma)$ has no complex strictly convex complexifications.

Received: 06.07.1999

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