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  • 1 Shiraz University of Technology Department of Mathematics Shiraz 71555 Iran
  • 2 Isfahan University of Technology Department of Mathematical Sciences Isfahan 84156-83111 Iran
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Abstract  

We study weakly compact left and right multipliers on the Banach algebra L0(

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)* of a locally compact group
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. We prove that
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is compact if and only if L0(
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)* has either a non-zero weakly compact left multiplier or a certain weakly compact right multiplier on L0(
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)*. We also give a description of weakly compact multipliers on L0(
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)* in terms of weakly completely continuous elements of L0t8(
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)*. Finally we show that
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is finite if and only if there exists a multiplicative linear functional n on L0(
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) such that n is a weakly completely continuous element of L0(
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)*

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