Strictly singular operators on the Baernstein and Schreier spaces

2025/09/10 by Laustsen, Niels Jakob, JamesSmith
#46B45 #46H10 #47L10 (primary) 46B03 #47L20 (secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2509.08796

Abstract

Every composition of two strictly singular operators is compact on the Baernstein space B_p for 1 < p < ∞ and on the p-convexified Schreier space S_p for 1 ≤ p < ∞. Furthermore, every subsymmetric basic sequence in B_p (respectively, S_p) is equivalent to the unit vector basis for ℓ_p (respectively, c₀), and the Banach spaces B_p and S_p contain block basic sequences whose closed span is not complemented.

Citations

• Closed ideals of operators on the Baernstein and Schreier spaces
• Equivalence of block sequences in Schreier spaces and their duals
• The number of closed ideals in L(L_p)
• Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces
• Classes of strictly singular operators and their products
• On the complemented subspaces of the Schreier spaces

Cited by

• Compactness of compositions of strictly singular operators on direct sums of Baernstein, Schreier and ℓ_p-spaces

Related

• Compactness of compositions of strictly singular operators on direct sums of Baernstein, Schreier and ℓ_p-spaces
• Equivalence of block sequences in Schreier spaces and their duals
• Strictly singular operators in Tsirelson like spaces
• Strictly singular non-compact diagonal operators on HI spaces
• Strictly singular operators in asymptotic ℓ_p Banach spaces