A disjointness type property of conditional expectation operators

Beata Randrianantoanina. "A disjointness type property of conditional expectation operators." Colloquium Mathematicae 102.1 (2005): 9-20. <http://eudml.org/doc/283426>.

@article{BeataRandrianantoanina2005,
abstract = {We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.},
author = {Beata Randrianantoanina},
journal = {Colloquium Mathematicae},
keywords = {band-preserving; Banach lattice; conditional expectation operator},
language = {eng},
number = {1},
pages = {9-20},
title = {A disjointness type property of conditional expectation operators},
url = {http://eudml.org/doc/283426},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Beata Randrianantoanina
TI - A disjointness type property of conditional expectation operators
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 1
SP - 9
EP - 20
AB - We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.
LA - eng
KW - band-preserving; Banach lattice; conditional expectation operator
UR - http://eudml.org/doc/283426
ER -