caa a22 4500 469068485 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02808215 doi (NATIONALLICENCE)springer-10.1007/BF02808215 Bourgain Jean Department of Mathematics, Institute des Hautes Etudes Sciences, 35 Route de Chartres, 91440, Bures-Sur-Yvette, France aut A remark on the behaviour of L p-multipliers and the range of operators acting on L p-spaces [Elektronische Daten] [Jean Bourgain] In this paper, new results are obtained concerning the uniform approximation property (UAP) inL p-spaces (p≠2,1,∞). First, it is shown that the "uniform approximation function” does not allow a polynomial estimate. This fact is rather surprising since it disproves the analogy between UAP-features and the presence of "large” euclidian subspaces in the space and its dual. The examples are translation invariant spaces on the Cantor group and this extra structure permits one to replace the problem with statements about the nonexistence of certain multipliers in harmonic analysis. Secondly, it is proved that the UAP-function has an exponential upper estimate (this was known forp=1, ∞). The argument uses Schauder's fix point theorem. Its precise behaviour is left unclarified here. It appears as a difficult question, even in the translation invariant context. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 79/2-3(1992-10-01), 193-206 0021-2172 79:2-3<193 1992 79 11856 https://doi.org/10.1007/BF02808215 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808215 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bourgain Jean Department of Mathematics, Institute des Hautes Etudes Sciences, 35 Route de Chartres, 91440, Bures-Sur-Yvette, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 79/2-3(1992-10-01), 193-206 0021-2172 79:2-3<193 1992 79 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer