Weyl numbers versus $Z$-Weyl numbers
Volume 223 / 2014
Studia Mathematica 223 (2014), 233-250
MSC: Primary 47B06.
DOI: 10.4064/sm223-3-4
Abstract
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.
