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The research aims to explore the Banach envelopes and duals of Lipschitz-free p-spaces where 0 < p < 1.

June 4, 2026Proceedings of the American Mathematical Society

On Banach envelopes and duals of Lipschitz-free 𝑝-spaces for 0<𝑝<1

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The research aims to explore the Banach envelopes and duals of Lipschitz-free p-spaces where 0 < p < 1.
Analyzed the structure of Lipschitz-free p-spaces.
Proved the one-to-one nature of the Banach envelope map for these spaces.
Investigated the implications for the dual space and its properties.
Demonstrated that the Banach envelope map of F_p(M) is one-to-one.
Established that the dual space of F_p(M) separates points of F_p(M).
Addressed a previously raised problem by the first author and Kalton.

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Implication

This note demonstrates the one-to-one nature of the Banach envelope map in Lipschitz-free p-spaces, highlighting implications for their linear structure.

Cite This Study

Albiac et al. (2026) studied this question.

synapsesocial.com/papers/6a2117bfd499ed480b1709a1 https://doi.org/10.1090/proc/17592

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Implication

This note demonstrates the one-to-one nature of the Banach envelope map in Lipschitz-free p-spaces, highlighting implications for their linear structure.

On Banach envelopes and duals of Lipschitz-free 𝑝-spaces for 0<𝑝<1

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Discussion

Implication

Cite This Study

On Banach envelopes and duals of Lipschitz-free 𝑝-spaces for 0<𝑝<1

Key Points

Discussion

Implication

Cite This Study

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