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Locally uniformly rotund norms
Author(s) -
Raja M.
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007816
Subject(s) - mathematics , norm (philosophy) , banach space , subspace topology , dual norm , generalization , pure mathematics , mathematical analysis , law , political science
Given a Banach space X and a norming subspace Z ⊂ X *, a geometrical method is introduced to characterize the existence of an equivalent σ( X, Z )‐lsc LUR norm on X . A new simple proof of the Theorem of Troyanski: every rotund space with a Kadec norm is LUR renormable , and a generalization of the Moltó, Orihuela and Troyanski characterization of the LUR renormability, are provided without probability arguments. Among other applications, it is shown that a dual Banach space with a w *‐Kadec norm admits a dual LUR norm.