Operators whose adjoints are quasi p-nuclear

J. M. Delgado, C. Piñeiro, and E. Serrano. "Operators whose adjoints are quasi p-nuclear." Studia Mathematica 197.3 (2010): 291-304. <http://eudml.org/doc/285627>.

@article{J2010,
abstract = {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 $K ⊆ \{∑ₙαₙxₙ: (αₙ) ∈ B_\{ℓ_\{p^\{\prime \}\}\}\}$. 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.},
author = {J. M. Delgado, C. Piñeiro, E. Serrano},
journal = {Studia Mathematica},
keywords = {-compact sets; -compact operator; weakly -compact operator; -summing operator; quasi -nuclear operator; -nuclear operator; relative -compactness; -summability; quasi -nuclearity; adjoint operator},
language = {eng},
number = {3},
pages = {291-304},
title = {Operators whose adjoints are quasi p-nuclear},
url = {http://eudml.org/doc/285627},
volume = {197},
year = {2010},
}

TY - JOUR
AU - J. M. Delgado
AU - C. Piñeiro
AU - E. Serrano
TI - Operators whose adjoints are quasi p-nuclear
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 3
SP - 291
EP - 304
AB - 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 $K ⊆ {∑ₙαₙxₙ: (αₙ) ∈ B_{ℓ_{p^{\prime }}}}$. 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.
LA - eng
KW - -compact sets; -compact operator; weakly -compact operator; -summing operator; quasi -nuclear operator; -nuclear operator; relative -compactness; -summability; quasi -nuclearity; adjoint operator
UR - http://eudml.org/doc/285627
ER -