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- W2164411312 abstract "For a locally compact (non-compact) group G , consider L ∞ ( G ) as a left module over the algebra L 1 ( G ) ∗∗ , endowed with the first Arens product. We answer in the affirmative a question raised by Hofmeier–Wittstock (Math. Ann. 308 (1) (1997) 141) concerning the automatic boundedness of the corresponding module homomorphisms on L ∞ ( G ) . In fact, we prove that an even stronger assertion holds true. Furthermore, we show that the theorem, first obtained by Ghahramani–McClure (Canad. Math. Bull. 35 (2) (1992) 180), on the automatic w ∗ -continuity of the (bounded) L ∞ ( G ) ∗ -module homomorphisms on L ∞ ( G ) , can be sharpened in a similar fashion. To this end, a general factorization theorem for bounded families in L ∞ ( G ) is proved from which we shall derive both results." @default.
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- W2164411312 date "2004-12-01" @default.
- W2164411312 modified "2023-10-17" @default.
- W2164411312 title "Solution to a conjecture by Hofmeier–Wittstock" @default.
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- W2164411312 doi "https://doi.org/10.1016/j.jfa.2004.02.013" @default.
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