| Abstrakt: |
Abstract: Let $(X,\|\cdot\|_X)$ be a real Banach space and let $E$ be an ideal of $L^0$ over a $\sigma$-finite measure space $(O,\Sigma,\mu)$. Let $(X)$ be the space of all strongly $\Sigma$-measurable functions $f O\to X$ such that the scalar function $\wtf$, defined by $\wtf(o)=\|f(o)\|_X$ for $o\in O$, belongs to $E$. The paper deals with strong topologies on $E(X)$. In particular, the strong topology $\beta(E(X), E(X)^\sim_n)$ ($E(X)^\sim_n=$ the order continuous dual of $E(X)$) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. |
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