Embeddings of Müntz Spaces in L^∞ ([STIX]x1D707). Issue 1 (9th January 2019) - Al Alam, Ihab; Lefèvre, Pascal
Abstract: In this paper, we discuss the properties of the embedding operator i_[STIX]x1D707^[STIX]x1D6EC:M_[STIX]x1D6EC^∞ L^∞ ([STIX]x1D707), where [STIX]x1D707 is a positive Borel measure on [0, 1] and M_[STIX]x1D6EC^∞ is a Müntz space. In particular, we compute the essential norm of this embedding. As a consequence, we recover some results of the first author. We also study the compactness (resp. weak compactness) and compute the essential norm (resp. generalized essential norm) of the embedding i_[STIX]x1D707_1, [STIX]x1D707_2:L^∞ ([STIX]x1D707_1)L^∞ ([STIX]x1D707_2), where [STIX]x1D707_1, [STIX]x1D707_2 are two positive Borel measures on [0, 1] with [STIX]x1D707_2 absolutely continuous with respect to [STIX]x1D707_1 .