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On balancedness and D-completeness of the space of semi-Lipschitz functions

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Abstract

Let (X, d) be a quasi-metric space and (Y, q) be a quasi-normed linear space. We show that the normed cone of semi-Lipschitz functions from (X, d) to (Y, q) that vanish at a point x 0 ∈ X, is balanced. Moreover, it is complete in the sense of D. Doitchinov whenever (Y, q) is a biBanach space.

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Authors and Affiliations

  1. E.T.S. Ingenieros de Caminos, Departamento de Matemática Aplicada, IUMPA-UPV, Universidad Politécnica de Valencia, 46071, Valencia, Spain

    S. Romaguera & J. M. Sánchez-Álvarez

  2. Departamento de Matemáticas, Universidad Jaume I, Campus de Riu Sec, 12071, Castellón, Spain

    M. Sanchis

Authors
  1. S. Romaguera
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  2. J. M. Sánchez-Álvarez
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  3. M. Sanchis
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Correspondence to S. Romaguera.

Additional information

The authors acknowledge the support of Plan Nacional I+D+I and FEDER, under grant MTM2006-14925-C02-01. The second listed author is also supported by a grant FPI from the Spanish Ministry of Education and Science.

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Romaguera, S., Sánchez-Álvarez, J.M. & Sanchis, M. On balancedness and D-completeness of the space of semi-Lipschitz functions. Acta Math Hung 120, 383–390 (2008). https://doi.org/10.1007/s10474-007-7159-2

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  • DOI: https://doi.org/10.1007/s10474-007-7159-2

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