Absolutely (r,p,q)-summing inclusions

Carsten Michels. "Absolutely (r,p,q)-summing inclusions." Studia Mathematica 178.1 (2007): 19-45. <http://eudml.org/doc/284492>.

@article{CarstenMichels2007,
abstract = {As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary Banach sequence spaces and inclusions between finite-dimensional Schatten classes. Finally, applications to Hilbert numbers of inclusions are given.},
author = {Carsten Michels},
journal = {Studia Mathematica},
keywords = {absolutely summing operators; Schatten classes; interpolation; Hilbert numbers; limit orders},
language = {eng},
number = {1},
pages = {19-45},
title = {Absolutely (r,p,q)-summing inclusions},
url = {http://eudml.org/doc/284492},
volume = {178},
year = {2007},
}

TY - JOUR
AU - Carsten Michels
TI - Absolutely (r,p,q)-summing inclusions
JO - Studia Mathematica
PY - 2007
VL - 178
IS - 1
SP - 19
EP - 45
AB - As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary Banach sequence spaces and inclusions between finite-dimensional Schatten classes. Finally, applications to Hilbert numbers of inclusions are given.
LA - eng
KW - absolutely summing operators; Schatten classes; interpolation; Hilbert numbers; limit orders
UR - http://eudml.org/doc/284492
ER -