Solvability of the functional equation f = (T-I)h for vector-valued functions

Ryotaro Sato. "Solvability of the functional equation f = (T-I)h for vector-valued functions." Colloquium Mathematicae 99.2 (2004): 253-265. <http://eudml.org/doc/285070>.

@article{RyotaroSato2004,
abstract = {Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and $lim_\{n→∞\} fₙ = f$ in measure for some f ∈ M(μ;X), then also $lim_\{n→∞\} Tfₙ = Tf$ in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying f = (T-I)h.},
author = {Ryotaro Sato},
journal = {Colloquium Mathematicae},
keywords = {reflexive Banach space; probability measure space; vector-valued function; null-preserving transformation; measure-preserving transformation; Lamperti-type operator; conservative; ergodicity; cohomology equation; coboundary},
language = {eng},
number = {2},
pages = {253-265},
title = {Solvability of the functional equation f = (T-I)h for vector-valued functions},
url = {http://eudml.org/doc/285070},
volume = {99},
year = {2004},
}

TY - JOUR
AU - Ryotaro Sato
TI - Solvability of the functional equation f = (T-I)h for vector-valued functions
JO - Colloquium Mathematicae
PY - 2004
VL - 99
IS - 2
SP - 253
EP - 265
AB - Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and $lim_{n→∞} fₙ = f$ in measure for some f ∈ M(μ;X), then also $lim_{n→∞} Tfₙ = Tf$ in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying f = (T-I)h.
LA - eng
KW - reflexive Banach space; probability measure space; vector-valued function; null-preserving transformation; measure-preserving transformation; Lamperti-type operator; conservative; ergodicity; cohomology equation; coboundary
UR - http://eudml.org/doc/285070
ER -