Sequence-singular operators

2015/09/04 by Gleb Sirotkin, Sirotkin, Gleb, Ben Wallis +1
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.FA #msc:46B06 #msc:46B25 #msc:46B45 #msc:47L10 #msc:47L20

paper · pdf · doi:10.48550/arxiv.1509.01485

13 pages

arxiv created 2015/09/04 · arxiv updated 2015/09/07

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 L(ℓ₁⊕ℓ_q), 1<q<∞, and L(ℓ₁⊕ c₀). This finishes answering a longstanding question of Pietsch.

Related

• Operator Ideals arising from Generating Sequences
• Representation of sequence classes by operator ideals
• Ideals in L(L₁)
• Closed ideals of operators acting on some families of sequence spaces
• K-theory for algebras of operators on Banach spaces