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Operators on the stopping time space

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Apatsidis D.

Studia Mathematica

2015

tom 228

nr 3

235-258

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 $ℳ (2^ℕ)$.

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1 Studia Mathematica

1 Apatsidis D.

1 2015

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Operators on the stopping time space