Bad properties of the Bernstein numbers
Volume 184 / 2008
Studia Mathematica 184 (2008), 263-269
MSC: Primary 47B06.
DOI: 10.4064/sm184-3-5
Abstract
We show that the classes $\mathfrak L_p^{\rm bern}:= \{ T : (b_n(T) ) \in l_p \}$ associated with the Bernstein numbers $b_n$ fail to be operator ideals. Moreover, $\mathfrak L_p^{\rm bern} \circ \mathfrak L_q^{\rm bern} \not\subseteq \mathfrak L_r^{\rm bern}$ for $1/r = 1/p + 1/q$.
