Convergence tensor products and a strict topology

Publisher： Cambridge University Press

E-ISSN： 1755-1633|21|2|281-301

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.21, Iss.2, 1980-05, pp. : 281-301

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Abstract

We are interested in the strict topology τ on , the set L(E, F) of all continuous linear mappings from E into a Banach space F endowed with the topology of pointwise convergence. The T3-completion of the convergence tensor product E c Lc F is the set of all τ-continuous linear functionals on L(E, F) and τ is the topology of uniform convergence on the compact subsets of . In the case that E is a nuclear Fréchet space, a nuclear (DF)-space or a Banach space with the bounded approximation property the topology τ agrees with the topology of Lco (E, F).

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