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Inclusion Theorems for K-Spaces

A sequence space is a vector subspace of the space ω of all real (or complex) sequences. A sequence space E with a locally convex topology τ is called a K- space if the inclusion map E → ω is continuous, when ω is endowed with the product topology . A K-space E with a Frechet (i.e., complete, metrizable and locally convex) topology is called an FK-space; if the topology is a Banach topology, then E is called a BK-space.