Publication: Sobre operadores y sucesiones en espacios de Banach separables
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1985
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Universidad de Murcia
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Abstract
Let B and X be Banach spaces, let B be reflexive, and let (an) be a sequence in B. The author shows that inf{∑|fan|:f∈B*,||f||=1}>0 if and only if the subspace {f∈B*:∑|fan|<∞} contains no closed infinite-dimensional subspace of B*, and in that case we have, for any bounded operator T:B→X,(i)T* is strictly singular whenever ∑Tan is weakly unconditionally Cauchy, and (ii) T is compact whenever ∑||Tan||<∞.
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X Jornadas Hispano-Lusas de Matemáticas, 21-25 de enero de 1985, Murcia, España.