The algebra of bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals

Andr\'as Zs\'ak; Thomas Schlumprecht

arxiv: 1409.3480 · v1 · pith:LQ4GYVPOnew · submitted 2014-09-11 · 🧮 math.FA

The algebra of bounded linear operators on ell_poplusell_q has infinitely many closed ideals

Thomas Schlumprecht , Andr\'as Zs\'ak This is my paper

classification 🧮 math.FA

keywords idealsalgebraboundedclosedinfinitelylinearmanyoperators

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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'.

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The algebra of bounded linear operators on ell_poplusell_q has infinitely many closed ideals

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