THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS

DOI10.1017/S1446788709000238zbMath1189.28009MaRDI QIDQ5189634

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Publication date: 17 March 2010

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

vector measureFatou propertyLebesgue topologyscalarly integrable functionFréchet space (lattice)

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Vector-valued set functions, measures and integrals (28B05) Topological lattices, etc. (topological aspects) (54H12) Locally convex Fréchet spaces and (DF)-spaces (46A04) Ordered topological linear spaces, vector lattices (46A40)

Related Items (3)

Extension and integral representation of the finite Hilbert transform in rearrangement invariant spaces ⋮ On the optimally defined Hardy operator in $L^p$-spaces ⋮ Topological duals of locally convex function spaces

Cites Work

• Operators into \(L^ 1\) of a vector measure and applications to Banach lattices
• The space of scalarly integrable functions for a Fréchet-space-valued measure
• Weighted inductive and projective limits of normed Köthe function spaces
• Vector measures and integration in non-complete spaces
• On the Fréchet space \(L_{p^-}\)
• Primary products of Banach spaces
• Locally convex spaces containing no copy of \(c_ 0\)
• Banach lattices with the Fatou property and optimal domains of kernel operators
• Exhaustive operators and vector measures
• Copies of 𝑐₀ and ℓ_{∞} in topological Riesz spaces
• On Subspaces of the Spaces L  locp and of Their Strong Duals
• On the Space l^p+ = ∩l^q_q>p
• The canonical spectral measure and köothe function spaces

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