, Volume 22, Issue 3-4, pp 247-256

The isometries ofC p

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Abstract

Theorem.Let 1≦p≦∞,p ≠ 2, and let V be an isometry of Cp onto itself. Then there exist two unitary operators u and w on l2 so that V acts on Cp in one of the following forms: \((i) Vx = u \cdot x \cdot w; (ii) Vx = u \cdot x^T \cdot w\) (where xT is the transpose of x).

This is a part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Prof. J. Lindenstrauss.