The algebra of bounded linear operators on ℓ_p⊕ℓ_q has infinitely many closed ideals

2014/09/11 by Thomas Schlumprecht, Schlumprecht, Thomas, András Zsák +1
Mathematics · #46B25 #47L20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B25 #msc:47L20

paper · pdf · doi:10.48550/arxiv.1409.3480

18 pages

arxiv created 2014/09/11 · arxiv updated 2014/09/12

Abstract

We prove that in the reflexive range 1<p<q<∞ the algebra of all bounded linear operators on ℓ_p⊕ℓ_q has infinitely many closed ideals. This solves a problem raised by A. Pietsch in his book `Operator ideals'.

Related

• Ideals in L(L₁)
• The M-ideal structure of some algebras of bounded linear operators
• The number of closed ideals in L(L_p)
• Approximate identities for Ideals in L(L^p))
• Ideals of operators on (⊕ ℓ^∞(n))_ℓ¹