Uniqueness of rotation invariant norms

If N [greater than or equal to] 2, then there exist finitely many rotations of the sphere [S.sup.N] such that the set of the corresponding rotation operators on [L.sup.p]([S.sup.N]) determines the norm topology for 1 < p [less than or equal to] [less than or equal to] [infinity]. For N = 1 the si...

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Bibliographic Details
Published inBanach journal of mathematical analysis Vol. 3; no. 1; pp. 85 - 98
Main Authors Alaminos, J., Extremera, J., Villena, A. R.
Format Journal Article
LanguageEnglish
Published Springer 2009
Subjects
Analysis
Invariants
United Kingdom
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Summary:If N [greater than or equal to] 2, then there exist finitely many rotations of the sphere [S.sup.N] such that the set of the corresponding rotation operators on [L.sup.p]([S.sup.N]) determines the norm topology for 1 < p [less than or equal to] [less than or equal to] [infinity]. For N = 1 the situation is different: the norm topology of [L.sup.2]([S.sup.1]) cannot be determined by the set of operators corresponding to the rotations by elements of any 'thin' set of rotations of [S.sup.1]. Key words and phrases. Automatic continuity, Dirichlet set, N-set, rotations of the sphere, strong Kazhdan's property, uniqueness of norm.
ISSN:1735-8787
1735-8787
DOI:10.15352/bjma/1240336426