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). |
Databáze: | Directory of Open Access Journals |
Externí odkaz: |