Operators on the stopping time space

• Autorzy: Dimitris Apatsidis
• Języki publikacji: EN

Abstrakty

EN

Let S¹ be the stopping time space and ℬ₁(S¹) be the Baire-1 elements of the second dual of S¹. To each element x** in ℬ₁(S¹) we associate a positive Borel measure $μ_{x**}$ on the Cantor set. We use the measures ${μ_{x**}: x** ∈ ℬ₁(S¹)}$ to characterize the operators T: X → S¹, defined on a space X with an unconditional basis, which preserve a copy of S¹. In particular, if X = S¹, we show that T preserves a copy of S¹ if and only if ${μ_{T**(x**)}: x** ∈ ℬ₁(S¹)}$ is non-separable as a subset of $ℳ (2^ℕ)$.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 228
• Numer: 3
• Strony: 235-258

Daty

wydano

2015

Twórcy

autor

Dimitris Apatsidis

• Faculty of Applied Sciences, National Technical University of Athens, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece

Identyfikatory

DOI

10.4064/sm228-3-3