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Sobre operadores y sucesiones en espacios de Banach separables

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Martín Peinador, Elena (1985) Sobre operadores y sucesiones en espacios de Banach separables. In X Jornadas hispano-lusas de matemáticas : sección de análisis matemático. Universidad de Murcia, Murcia, pp. 380-384.

Official URL: http://cisne.sim.ucm.es/record=b2196627~S6*spi


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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||<∞.


Item Type:Book Section
Additional Information:

X Jornadas Hispano-Lusas de Matemáticas, 21-25 de enero de 1985, Murcia, España.

Subjects:Sciences > Mathematics > Mathematical analysis
Sciences > Mathematics > Topology
ID Code:22032
Deposited On:20 Jun 2013 14:58
Last Modified:12 Dec 2018 15:14

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