Generalized mixed topology on F-normed function spaces

• Autorzy: Kasior E. , Nowak M.
• Języki publikacji: EN

Abstrakty

EN

Let (X, ||•||) be a F-normed function space over a σ-finite measure space (Ω, Σ, μ) and let ||•||₀ denote the usual F-norm on L⁰ that generates the convergence in measure on subsets of finite measures. In X a natural two-normed convergence can be defined as follows: a sequence (x_n) in X is said to be γ-convergent to x ϵ X whenever || x_n - x||₀ → 0 and sup_n||x_n|| < ∞. In this paper we study locally solid topologies on X satisfying the continuity property with respect to this γ-convergence in X. We call such topologies "uniformly Lebesgue". These investigations are closely related to the theory of generalized inductive limit topologies in the sense of Turpin. In particular we show that a generalized mixed topology γ_T(T_φ, T₀|_L^φ) on the Orlicz space L^φ (φ is not assumed to be convex) is the finest uniformly Lebesgue topology on L^φ. Moreover, we characterize γ_φ-linear functionals on L^φ.

Słowa kluczowe

EN

function spaces; Orlicz spaces; generalized mixed topologies; two-norm convergence; uniformly Lebesgue topologies

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr 1
• Strony: 55--66
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Kasior E.

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin 3, Poland

autor

Nowak M.

• Institute of Mathematics, University of Zielona Góra, Szafrana 4 A, 65-516 Zielona Góra, Poland

Bibliografia

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