The algebra of bounded linear operators on ${\ell }_p\oplus {\ell }_q$ has infinitely many closed ideals

Abstract

We prove that in the reflexive range $1<p<q<\infty$ the algebra of all bounded linear operators on ${\ell }_p\oplus {\ell }_q$ has infinitely many closed ideals. This solves a problem raised by A. Pietsch in his book `Operator ideals'.

arXiv comment18 pages

Cited by in corpus (2)

• Closed ideals in $\mathcal{L}(X)$ and $\mathcal{L}(X^{\ast })$ when $X$ contains certain copies of ${\ell }_p$ and $c_0$
• Sequence-singular operators