The ideal of p-compact operators: a tensor product approach

Daniel Galicer, Silvia Lassalle, and Pablo Turco. "The ideal of p-compact operators: a tensor product approach." Studia Mathematica 211.3 (2012): 269-286. <http://eudml.org/doc/285912>.

@article{DanielGalicer2012,
abstract = {We study the space of p-compact operators, $_\{p\}$, using the theory of tensor norms and operator ideals. We prove that $_\{p\}$ is associated to $/d_\{p\}$, the left injective associate of the Chevet-Saphar tensor norm $d_\{p\}$ (which is equal to $g_\{p^\{\prime \}\}^\{\prime \}$). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that $_\{p\}(E;F)$ is equal to $_\{q\}(E;F)$ for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of $_\{p\}$. For instance, we show that $_\{p\}$ is regular, surjective, and totally accessible, and we characterize its maximal hull $_\{p\}^\{max\}$ as the dual ideal of p-summing operators, $Π_\{p\}^\{dual\}$. Furthermore, we prove that $_\{p\}$ coincides isometrically with $_\{p\}^\{dual\}$, the dual to the ideal of the quasi p-nuclear operators.},
author = {Daniel Galicer, Silvia Lassalle, Pablo Turco},
journal = {Studia Mathematica},
keywords = {tensor norms; -compact operators; quasi -nuclear operators; absolutely -summing operators; approximation properties},
language = {eng},
number = {3},
pages = {269-286},
title = {The ideal of p-compact operators: a tensor product approach},
url = {http://eudml.org/doc/285912},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Daniel Galicer
AU - Silvia Lassalle
AU - Pablo Turco
TI - The ideal of p-compact operators: a tensor product approach
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 3
SP - 269
EP - 286
AB - We study the space of p-compact operators, $_{p}$, using the theory of tensor norms and operator ideals. We prove that $_{p}$ is associated to $/d_{p}$, the left injective associate of the Chevet-Saphar tensor norm $d_{p}$ (which is equal to $g_{p^{\prime }}^{\prime }$). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that $_{p}(E;F)$ is equal to $_{q}(E;F)$ for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of $_{p}$. For instance, we show that $_{p}$ is regular, surjective, and totally accessible, and we characterize its maximal hull $_{p}^{max}$ as the dual ideal of p-summing operators, $Π_{p}^{dual}$. Furthermore, we prove that $_{p}$ coincides isometrically with $_{p}^{dual}$, the dual to the ideal of the quasi p-nuclear operators.
LA - eng
KW - tensor norms; -compact operators; quasi -nuclear operators; absolutely -summing operators; approximation properties
UR - http://eudml.org/doc/285912
ER -