Given an infinite-dimensional Banach space Z (substituting the Hilbert space ℓ₂), 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-3-4,
author = {Bernd Carl and Andreas Defant and Doris Planer},
title = {Weyl numbers versus Z-Weyl numbers},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {233-250},
zbl = {1325.47043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-3-4}
}
Bernd Carl; Andreas Defant; Doris Planer. Weyl numbers versus Z-Weyl numbers. Studia Mathematica, Tome 223 (2014) pp. 233-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-3-4/