标题：Multipliers on <mml:math alttext="$L(S)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, <mml:math alttext="$L(S)^{**}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>*</mml:mo><mml:mo>*</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>, and <mml:math alttext="$\mathit{LUC}(S)^{*}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi><mml:mi>U</mml:mi><mml:mi>C</mml:mi><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math> for a locally compact topological semigroup
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2002
卷号：29
DOI：10.1155/S016117120200652X
出版社：Hindawi Publishing Corporation
摘要：We study compact and weakly compact multipliers on
L(S), L(S)**, and LUC(S)*, where the latter is the dual of LUC(S). We show that a left cancellative semigroup S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on L(S)**. We also prove that S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on LUC(S)*.
