ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47B65 Grobler, Jacobus Potchefstroom University for CHE, South Africa The polar decomposition of disjointness preserving operators. It is shown that if E and F are complex Riesz spaces, if T is an order bounded disjointness preserving operator from E into F and if F has the Z-extension property for principal ideals, then there exists an injective orthomorphism S̃ on the ideal generated in F by the range of T such that T z = S̃|T |z for all z ∈ E. Moreover, we have that |S̃| = I and that S̃ can be extended (with retention of properties) to an orthomorphism on F if F is Dedekind complete. The latter result is known and derived by Hahn-Banach extension type theorems. Reference: P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin Heidelberg New York, 1991.