Sequence-singular operators

Abstract

In this paper we study two types of collections of operators on a Banach space on the subject of forming operator ideals. One of the types allows us to construct an uncountable chain of closed ideals in each of the operator algebras $\mathcal{L}({\ell }_1\oplus {\ell }_q)$, $1<q<\infty$, and $\mathcal{L}({\ell }_1\oplus c_0)$. This finishes answering a longstanding question of Pietsch.

13 pages

References in corpus (3)

• The algebra of bounded linear operators on ${\ell }_p\oplus {\ell }_q$ has infinitely many closed ideals
• Classes of operators determined by ordinal indices
• Closed ideals in $\mathcal{L}(X)$ and $\mathcal{L}(X^{\ast })$ when $X$ contains certain copies of ${\ell }_p$ and $c_0$