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

• Autorzy: Ryotaro Sato
• Języki publikacji: EN

Abstrakty

EN

Let X be a reflexive Banach space and (Ω,𝓐,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,𝓐,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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 99
• Numer: 2
• Strony: 253-265

Daty

wydano

2004

Twórcy

autor

Ryotaro Sato

• Department of Mathematics, Okayama University, Okayama, 700-8530 Japan

Identyfikatory

DOI

10.4064/cm99-2-9