Weakly compact multipliers on Banach algebras related to a locally compact group

作者：Mehdipour M J^*; Nasr Isfahani R

来源：Acta Mathematica Hungarica, 2010, 127(3): 195-206.

DOI：10.1007/s10474-010-9117-7

• locally compact group
• multiplier
• weakly compact operator
• weakly completely continuous element

We study weakly compact left and right multipliers on the Banach algebra L(0)(infinity)(G)* of a locally compact group G. We prove that G is compact if and only if L(0)(infinity)(G)* has either a non-zero weakly compact left multiplier or a certain weakly compact right multiplier on L(0)(infinity)(G)*. We also give a description of weakly compact multipliers on L(0)(infinity)(G)* in terms of weakly completely continuous elements of L(0)(infinity)(G)*. Finally we show that G is finite if and only if there exists a multiplicative linear functional non L(0)(infinity)(G)* such that n is a weakly completely continuous element of L(0)(infinity)(G)*.

• 出版日期2010-5