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

Thomas Schlumprecht, András Zsák

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 rai…