Operators on the stopping time space

Dimitris Apatsidis. "Operators on the stopping time space." Studia Mathematica 228.3 (2015): 235-258. <http://eudml.org/doc/285424>.

@article{DimitrisApatsidis2015,
abstract = {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 $ℳ (2^ℕ)$.},
author = {Dimitris Apatsidis},
journal = {Studia Mathematica},
keywords = {Baire-$1$ elements; complemented subspace; dyadic tree; -embedding; isomorphism; stopping time space; unconditionnal basis},
language = {eng},
number = {3},
pages = {235-258},
title = {Operators on the stopping time space},
url = {http://eudml.org/doc/285424},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Dimitris Apatsidis
TI - Operators on the stopping time space
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 3
SP - 235
EP - 258
AB - 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 $ℳ (2^ℕ)$.
LA - eng
KW - Baire-$1$ elements; complemented subspace; dyadic tree; -embedding; isomorphism; stopping time space; unconditionnal basis
UR - http://eudml.org/doc/285424
ER -