Geodesic
Strong topologies on vector-valued function spaces
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 401-414

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Let $(X,\Vert \cdot \Vert _X)$ be a real Banach space and let $E$ be an ideal of $L^0$ over a $\sigma $-finite measure space $(Ø,\Sigma ,\mu )$. Let $(X)$ be the space of all strongly $\Sigma $-measurable functions $f\: Ø\rightarrow X$ such that the scalar function ${\widetilde{f}}$, defined by ${\widetilde{f}}(ø)=\Vert f(ø)\Vert _X$ for $ø\in Ø$, 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.
Classification : 46A40, 46E30, 46E40
Keywords: vector valued function spaces; locally solid topologies; strong topologies; Mackey topologies; absolute weak topologies 
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     author = {Nowak, Marian},
     title = {Strong topologies on vector-valued function spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {401--414},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2000},
     mrnumber = {1761397},
     zbl = {1050.46513},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000__50_2_a14/}
}
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Nowak, Marian. Strong topologies on vector-valued function spaces. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 401-414. http://geodesic.mathdoc.fr/item/CMJ_2000__50_2_a14/