2011
DOI: 10.1002/mana.200810163
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Sequential w‐right continuity and summing operators

Abstract: We continue the study of the w-right and strong * topologies in general Banach spaces started in [36,37] and [35]. We show that in L1 (μ)-spaces the w-right convergence of sequences admits a simpler control. Some considerations about these topologies will be contemplated in the particular cases of C*-algebras and JB*-triples in connection with summing operators. We also study (sequential) w-right-norm and strong*-norm continuity for holomorphic mappings. and the second author of the present note introduced in … Show more

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Cited by 6 publications
(4 citation statements)
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“…where E * denotes the topological dual of E and B E * represents its closed unit ball (for the theory of absolutely summing operators we refer to [20] and, for recent results, [14,21] and references therein). The space of all absolutely (q; p)-summing operators from E to F is denoted by Π q;p (E; F ) (or Π p (E; F ) if p = q).…”
Section: Preliminaries and Backgroundmentioning
confidence: 99%
See 1 more Smart Citation
“…where E * denotes the topological dual of E and B E * represents its closed unit ball (for the theory of absolutely summing operators we refer to [20] and, for recent results, [14,21] and references therein). The space of all absolutely (q; p)-summing operators from E to F is denoted by Π q;p (E; F ) (or Π p (E; F ) if p = q).…”
Section: Preliminaries and Backgroundmentioning
confidence: 99%
“…where E * denotes the topological dual of E and B E * represents its closed unit ball (for the theory of absolutely summing operators we refer to [20] and, for recent results, [14,21] and references therein).…”
Section: Preliminaries and Backgroundmentioning
confidence: 99%
“…The space of all absolutely p-summing linear operators from X to Y is represented by Π p (X; Y ). We refer the interested reader to [9,15,16] for more recent results and further details. A famous result due to Grothendieck asserts that every continuous linear operator from 1 to 2 is absolutely p-summing, regardless of the p ≥ 1.…”
Section: Introductionmentioning
confidence: 99%
“…A continuous linear operator u : X → Y is absolutely p-summing (we write u ∈ Π p (X; Y )) if (u(x j )) ∞ j=1 ∈ ℓ p (Y ) whenever (x j ) ∞ j=1 ∈ ℓ p,w (X) . For details we refer to the classical monograph [8] and to [4,9] for more recent results.…”
Section: Introductionmentioning
confidence: 99%