Functional analysis on normed spaces: the Banach space comparison

M. Sioen, S. Verwulgen

It is the aim of this paper to compute the category of Eilenberg-Moore algebras for the monad arising from the dual unit-ball functor on the category of (semi)normed spaces. We show that this gives rise to a stronger algebraic structure than the totally convex one obtained from the closed unit ball functor on the category of Banach spaces.

Keywords: Banach space, Monad, Totally convex module, Duality

2000 MSC: 46B04, 46M99, 52A01

Theory and Applications of Categories, Vol. 18, 2007, No. 3, pp 102-117.

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