Isometries between injective tensor products of Banach spaces

Krzysztof Jarosz

Vol. 121 (1986), No. 2, 383–396

DOI: 10.2140/pjm.1986.121.383

Abstract

Let K, H be real Banach spaces with strictly convex duals, and let X, Y be any real Banach spaces. In this paper we find a general form of isometries between the Banach spaces X⊗K and Y ⊗H. As a consequence we obtain that X⊗K and Y ⊗K are isometric if and only if X and Y are isometric. We also derive a theorem characterizing Banach spaces with a trivial centralizer.

Mathematical Subject Classification 2000

Primary: 46B20

Secondary: 46M05

Milestones

Received: 10 May 1983

Revised: 14 April 1984

Published: 1 February 1986