- 期刊
THE CONVOLUTION-INDUCED TOPOLOGY ON L_∞ (G) AND LINEARLY DEPENDENT TRANSLATES IN L_I (G)
並列摘要
Given a locally compact Hausdorff group G, we consider on L_∞(G)the τ_c-topology, i.e. the weak topology under all convolution operators induced by functions in L_1(G). As a major result we characterize the trigonometric polynomials on a compact group as those functions in L_1(G) whose left translates are contained in a finite-dimensional set. From this, we deduce that τ_c is different from the w^∗-topology on L_∞(G) whenever G is infinite. As another result, we show that τ_c coincides with the norm-topology if and only if G is discrete. The properties of τ_c are then studied further and we pay attention to the τ_c-almost periodic elements of L_∞(G).
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