A criterion for $2^\mathfrak{c}$ operator ideals on Banach spaces

Anna Pelczar-Barwacz (Jagiellonian U, Krakow)

Mar 18. 2025, 11:45 — 12:05

We present a general criterion based on the asymptotic behavior of basic sequences and Johnson-Schechtman technique, which guarantees large cardinality of the lattice of closed operator ideals in the algebra of bounded operators on a Banach space. The method yields $2^\mathfrak{c}$ closed operator ideals on a class of Lorentz sequence spaces, combinatorial spaces defined by compact families of finite subsets of integers, and spaces built on their basis - their $p$-convex versions and Baernstein spaces (extending the results of R.M.Causey - APB, N.J.Laustsen – J.Smith, A.Manoussakis - APB) and provides another approach to case of Rosenthal spaces, solved by W.B.Johnson and G.Schechtman.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Structures in Banach Spaces (Workshop)
Organizer(s):
Antonio Aviles (U Murcia)
Vera Fischer (U of Vienna)
Grzegorz Plebanek (U of Wroclaw)
Damian Sobota (U of Vienna)