Juan Carlos Ferrando (Operations Research Center, University Miguel Hernández of Elche) and Jerzy Kąkol (Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense, Madrid)

Abstract: The paper continues the study on the distinguished property of the space Cp(X) (of real-valued continuous functions over a Tychonoff space X in the pointwise topology) under the formation of tensor products towards the following research directions: (i) the injective tensor product Cp(X)⊗εE of Cp(X) and a real locally convex space E (and its completion Cp(X)⊗^εE), and (ii) the space Cp(X,E) of all E-valued continuous functions (with a normed space E) endowed with the pointwise topology. This work leads also to a new characterization of distinguished Fréchet locally convex spaces E. We show, e.g., that if Cp(X) is metrizable, then E is distinguished if and only if metrizable Cp(X)⊗εE is distinguished.