On balancedness and D-completeness of the space of semi-Lipschitz functions |
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| Authors: | Email author" target="_blank">S?RomagueraEmail author J?M?Sánchez-álvarez M?Sanchis |
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| Institution: | (1) E.T.S. Ingenieros de Caminos, Departamento de Matemática Aplicada, IUMPA-UPV, Universidad Politécnica de Valencia, 46071 Valencia, Spain;(2) Departamento de Matemáticas, Universidad Jaume I, Campus de Riu Sec, 12071 Castellón, Spain |
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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.
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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| Keywords: | and phrases" target="_blank"> and phrases semi-Lipschitz function quasi-normed linear space quasi-metric balanced biBanach D-complete |
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