On Laurent Operators on I,
نویسنده
چکیده
According to Steckin [4], the operator F on lp is bounded for every fixed p > 1, that is, (4) and (5) imply that y exists and is in lp and that (6) ||y||, ^ Const. ||*||,. Furthermore, the norm \\f\\p of F (that is, the least Const, satisfying (6)) is subject to an inequality of the type (7) \\F(f)\\P = 5,11/H, where Bp is an absolute constant, depending only on p. In what follows, p > 1 is fixed and F is considered as an operation x—>y = Fx of the Banach space lp into itself. Correspondingly, the subscript p on the norms || • • • ||P will be omitted. Note that (1), (4), Parseval's relation and the boundedness of F(f) show that (8) F(f X) = F(f) X7 Received by the editors February 27, 1956. 45
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تاریخ انتشار 2010