The convolution-induced topology on L∞(G) and linearly dependent translates in L1(G)

Autor: G. Crombez, W. Govaerts
Jazyk: angličtina
Rok vydání: 1982
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 5, Iss 1, Pp 11-20 (1982)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171282000027
Popis: Given a locally compact Hausdorff group G, we consider on L∞(G) the τc-topology, i.e. the weak topology under all convolution operators induced by functions in L1(G). As a major result we characterize the trigonometric polynomials on a compact group as those functions in L1(G) whose left translates are contained in a finite-dimensional set. From this, we deduce that τc is different from the w∗-topology on L∞(G) whenever G is infinite. As another result, we show that τc coincides with the norm-topology if and only if G is discrete. The properties of τc are then studied further and we pay attention to the τc-almost periodic elements of L∞(G).
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