Uniqueness of rotation invariant norms

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URI: http://hdl.handle.net/10481/32997
ISSN: 1735-8787
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Autor
Alaminos Prats, Jerónimo; Extremera Lizana, José; Villena Muñoz, Armando
Editorial
Tusi Mathematical Research Group
Materia
Rotations of the sphere
 
Automatic continuity
 
N-set
 
Dirichlet set
 
Strong Kazhdan's property
 
Uniqueness of norm
 
Fecha
2009
Referencia bibliográfica
Alaminos, J.; Extremera, J.; Villena, A.R. Uniqueness of rotation invariant norms. Banach Journal fo Mathematical Analysis, 3(1): 85-98 (2009). [http://hdl.handle.net/10481/32997]
Patrocinador
The authors were supported by MEC (Spain) Grant MTM2006-04837 and Junta de Andalucía Grants FQM-185 and Proyecto de Excelencia P06-FQM-01438.
Resumen
If N >= 2, then there exist finitely many rotations of the sphere S(N) such that the set of the corresponding rotation operators on L(p)(S(N)) determines the norm topology for 1 < p <= infinity. For N = 1 the situation is different: the norm topology of L(2)(S(1)) cannot be determined by the set of operators corresponding to the rotations by elements of any 'thin' set of rotations of S(1).
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