The representation of norm-continuous multipliers on 𝐿^{∞}-spaces

Hively, Gregory A.

doi:10.1090/S0002-9947-1973-0346425-2

The representation of norm-continuous multipliers on $L^{\infty }$-spaces
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by Gregory A. Hively

Trans. Amer. Math. Soc. 184 (1973), 343-353

DOI: https://doi.org/10.1090/S0002-9947-1973-0346425-2

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Abstract:

If G is a group and ${\mathcal {L}^\infty }(G,\mathcal {S})$ is an appropriate space of bounded measurable functions on G, a representation is obtained for the algebra of norm-continuous multipliers on ${\mathcal {L}^\infty }(G,\mathcal {S})$ as an algebra of bounded additive set functions on G. If G is a locally compact group, a representation of the norm-continuous multipliers on the quotient space ${\mathcal {L}^\infty }(G)$ is obtained in terms of a quotient algebra of bounded additive set functions on G.

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