Given an infinite-dimensional Banach space $Z$ (substituting the Hilbert space $\ell _2$), the $s$-number sequence of $Z$-Weyl numbers is generated by the approximation numbers according to the pattern of the classical Weyl numbers. We compare Weyl numbers with $Z$-Weyl numbers—a problem originally posed by
A. Pietsch. We recover a result of Hinrichs and the first author showing that the Weyl numbers are in a sense minimal. This emphasizes the outstanding role of Weyl numbers within the theory of eigenvalue distribution of operators between Banach spaces.
Keywords:
given infinite dimensional banach space substituting hilbert space ell s number sequence z weyl numbers generated approximation numbers according pattern classical weyl numbers compare weyl numbers z weyl numbers problem originally posed nbsp pietsch recover result hinrichs first author showing weyl numbers sense minimal emphasizes outstanding role weyl numbers within theory eigenvalue distribution operators between banach spaces
Affiliations des auteurs :
Bernd Carl
1
;
Andreas Defant
2
;
Doris Planer
3
1
Mathematisches Institut FSU Jena Ernst-Abbe-Platz 1–3 D-07743 Jena, Germany
2
Institut für Mathematik Carl von Ossietzky Universität Postfach 2503 D-26111 Oldenburg, Germany
3
Fachbereich Grundlagenwissenschaften Ernst-Abbe-Fachhochschule Jena Postfach 100314 D-07743 Jena, Germany
@article{10_4064_sm223_3_4,
author = {Bernd Carl and Andreas Defant and Doris Planer},
title = {Weyl numbers versus $Z${-Weyl} numbers},
journal = {Studia Mathematica},
pages = {233--250},
year = {2014},
volume = {223},
number = {3},
doi = {10.4064/sm223-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm223-3-4/}
}
TY - JOUR
AU - Bernd Carl
AU - Andreas Defant
AU - Doris Planer
TI - Weyl numbers versus $Z$-Weyl numbers
JO - Studia Mathematica
PY - 2014
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EP - 250
VL - 223
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm223-3-4/
DO - 10.4064/sm223-3-4
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%A Andreas Defant
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%J Studia Mathematica
%D 2014
%P 233-250
%V 223
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm223-3-4/
%R 10.4064/sm223-3-4
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Bernd Carl; Andreas Defant; Doris Planer. Weyl numbers versus $Z$-Weyl numbers. Studia Mathematica, Tome 223 (2014) no. 3, pp. 233-250. doi: 10.4064/sm223-3-4
