A spaceability result in the context of hypergroups


In this paper, by an elementary constractive technique, it is shown that L^r(\mathbb{Z}_+)-\bigcup_{q<r}L^q(\mathbb{Z}_+) is non-empty, where \mathbb{Z}_+ is the dual of a compact countable hypergroup introduced by Dunkl and Ramirez. Also, we prove that for each r>1, L^r(\mathbb{Z}_+)-\bigcup_{q<r}L^q(\mathbb{Z}_+) is spaceable.

DOI Code: 10.1285/i15900932v38n1p17

Keywords: locally compact hypergroup; spaceability; $L^p$-space

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