Abstract
Properties of spectral synthesis are exploited to show that, for a large class of commutative hypergroups and for every compact hypergroup, every closed, reflexive, left-translation-invariant subspace of L∞(K) is finite-dimensional. Also, we show that, for a class of hypergroups which includes many commutative hypergroups and all Z-hypergroups, every derivation of L1(K) into an arbitrary Banach L1-bimodule is continuous.
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