Displaying similar documents to “On Characterizations of Nuclear Spaces and Quasi-Integral Operators.”

Operators whose adjoints are quasi p-nuclear

J. M. Delgado, C. Piñeiro, E. Serrano (2010)

Studia Mathematica

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For p ≥ 1, a set K in a Banach space X is said to be relatively p-compact if there exists a p-summable sequence (xₙ) in X with K ⊆ ∑ ₙ α ₙ x ₙ : ( α ₙ ) ∈ B ℓ p ' . We prove that an operator T: X → Y is p-compact (i.e., T maps bounded sets to relatively p-compact sets) iff T* is quasi p-nuclear. Further, we characterize p-summing operators as those operators whose adjoints map relatively compact sets to relatively p-compact sets.