The strong "zero-two" law for positive contractions of Banach-Kantorovich L_p-lattices

TL;DR

This paper establishes a strong 'zero-two' law for positive contractions on Banach-Kantorovich Lp-lattices, advancing the understanding of operator behavior in these measure-valued function spaces.

Contribution

It introduces a new strong 'zero-two' law for positive contractions on Banach-Kantorovich Lp-lattices, utilizing measurable bundle methods.

Findings

Proves the strong 'zero-two' law for positive contractions.

Uses measurable bundle techniques to analyze operators.

Extends classical results to Banach-Kantorovich lattice setting.

Abstract

In the present paper we study majorizable operators acting on Banach-Kantorovich $L_p$-lattices, constructed by a measure $m$ with values in the ring of all measurable functions. Then using methods of measurable bundles of Banach-Kantorovich lattices, we prove the strong "zero-two" law for positive contractions of the Banach-Kantorovich $L_p$-lattices.