Geodesic
Embeddings of Müntz Spaces in $L^{\infty }(\unicode[STIX]{x1D707})$
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 1-9

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DOI

In this paper, we discuss the properties of the embedding operator $i_{\unicode[STIX]{x1D707}}^{\unicode[STIX]{x1D6EC}}:M_{\unicode[STIX]{x1D6EC}}^{\infty }{\hookrightarrow}L^{\infty }(\unicode[STIX]{x1D707})$, where $\unicode[STIX]{x1D707}$ is a positive Borel measure on $[0,1]$ and $M_{\unicode[STIX]{x1D6EC}}^{\infty }$ 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 $i_{\unicode[STIX]{x1D707}_{1},\unicode[STIX]{x1D707}_{2}}:L^{\infty }(\unicode[STIX]{x1D707}_{1}){\hookrightarrow}L^{\infty }(\unicode[STIX]{x1D707}_{2})$, where $\unicode[STIX]{x1D707}_{1}$, $\unicode[STIX]{x1D707}_{2}$ are two positive Borel measures on [0, 1] with $\unicode[STIX]{x1D707}_{2}$ absolutely continuous with respect to $\unicode[STIX]{x1D707}_{1}$.
DOI : 10.4153/CMB-2018-031-8
Mots-clés : Müntz space, embedding, essential norm, compact operator 
Alam, Ihab Al; Lefèvre, Pascal. Embeddings of Müntz Spaces in $L^{\infty }(\unicode[STIX]{x1D707})$. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 1-9. doi: 10.4153/CMB-2018-031-8
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     author = {Alam, Ihab Al and Lef\`evre, Pascal},
     title = {Embeddings of {M\"untz} {Spaces} in $L^{\infty }(\unicode[STIX]{x1D707})$},
     journal = {Canadian mathematical bulletin},
     pages = {1--9},
     year = {2019},
     volume = {62},
     number = {1},
     doi = {10.4153/CMB-2018-031-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-031-8/}
}
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%J Canadian mathematical bulletin
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