Henstock–Kurzweil Vector Distributions

Pérez-Becerra, Tomás; Sánchez-Perales, Salvador; Escamilla-Reyna, Juan A.

doi:10.1007/s00009-020-01612-5

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2023

2024

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“…It is known that for any Banach space X, the spaces of the Henstock integrable H([a, b], X) and Kurzweil integrable K([a, b], X) functions are not complete with the Alexiewicz seminorm ( [Fed03]). In [PBSPER20] Perez et al proved that the completion of the spaces H([a, b], X) and K([a, b], X) is a subspace of vector distributions and they defined an integral on the completion, which is known as the Henstock-Kurzweil vector distributional integral.…”

Section: Introductionmentioning

confidence: 99%

Topological properties of the space of integrable Henstock-Kurzweil vector distributions.

Escamilla-Rocha,

Alanís-López,

Escamilla-Reyna

2023

Preprint

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In this work, we prove that the space of integrable Henstock-Kurzweil vector distributions denoted as DHK([a,b],X) has a complemented copy of c0. We show conditions for DHK([a,b],X) to have a complemented copy of l1 and a copy of l∞. We also give conditions for DHK([a,b],X) to have property (V) and the Dieudonné property. Furthermore, we prove that DHK([a,b],X) does not have property (u). Mathematics Subject Classification (2010). Primary 26A39, 58A30; Secondary 46B03, 46B04.

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Section: Introductionmentioning

confidence: 99%