Abstract
We give an abstract Banach-Steinhaus theorem for locally convex spaces having suitable algebras of linear projections modelled on a σ-finite measure space. This theorem is applied to deduce barrelledness results for the space L∞ (μ, E) of essentially bounded and μ-measurable functions from a Radon measure space (Ω, σ, μ) into a locally convex space E and also for B (μ, E), the closure of the space of simple functions. Sample: if μ is atomless, then B (μ, E) is barrelled if and only if E is quasi-barrelled and E′(β (E′, E)) has the property (B) of Pietsch.
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This research has been supported by La Consejería de Educación y Ciencia. de la Junta de Andalucía.
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Díaz, S., Fernández, A., Florencio, M. et al. An Abstract Banach-Steinhaus Theorem and Applications to Function Spaces. Results. Math. 23, 242–250 (1993). https://doi.org/10.1007/BF03322300
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DOI: https://doi.org/10.1007/BF03322300