This article is cited in 3 papers

An Analytic Representation of the $L_0$-Valued Homomorphisms in the Orlicz–Kantorovich Modules

B. S. Zakirov

Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan

Abstract: We consider the Orlicz–Kantorovich modules $L_M(\nabla,m)$ associated with a complete Boolean algebra $\nabla$, an $N$-function $M$, and a measure $m$ defined on $\nabla$ and taking values in the algebra $L_0$ of all measurable real functions. We obtain an analytic representation of the continuous $L_0$-valued homomorphisms defined on such modules.

Key words: Banach–Kantorovich space, Banach module, conjugate Banach module.

UDC: 517.98

Received: 19.02.2007

 English version: Siberian Advances in Mathematics, 2009, 19:2, 128–149

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