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The n -dual space of the space of p -summable sequences

Yosafat E. P. Pangalela, Hendra Gunawan (2013)

Mathematica Bohemica

In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an n -normed space, we are interested in bounded multilinear n -functionals and n -dual spaces. The concept of bounded multilinear n -functionals on an n -normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear n -functionals, introduce the concept of n -dual spaces, and...

The non-archimedian space BC(X) with the strict topology.

Nicole De Grande-De Kimpe, Samuel Navarro (1994)

Publicacions Matemàtiques

Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.

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