cesàro spaces
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2021 ◽  
Vol 39 (1) ◽  
pp. 157-167
Author(s):  
G. Canan Hazar Güleç ◽  
M. Ali Sarıgöl

In this study we establish some identities or estimates for operator norms and the Hausdorff measure of noncompactness of certain operators on spaces |C_{α}|_{k}, which have more recently been introduced in [14]. Further, by applying the Hausdorff measure of noncompactness, we establish the necessary and sufficient conditions for such operators to be compact and so the some well known results are generalized.


Author(s):  
H. Roopaei ◽  
D. Foroutannia ◽  
M. İlkhan ◽  
E. E. Kara

2020 ◽  
Vol 191 (3) ◽  
pp. 487-512
Author(s):  
José Bonet ◽  
Werner J. Ricker
Keyword(s):  

2019 ◽  
Vol 71 (03) ◽  
pp. 501-532
Author(s):  
Sergey V. Astashkin ◽  
Karol Lesnik ◽  
Lech Maligranda

AbstractWe investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space $\text{Ces}_{\infty }$ and its sequence counterpart $\text{ces}_{\infty }$ are isomorphic. This is rather surprising since $\text{Ces}_{\infty }$ (like Talagrand’s example) has no natural lattice predual. We prove that $\text{ces}_{\infty }$ is not isomorphic to $\ell _{\infty }$ nor is $\text{Ces}_{\infty }$ isomorphic to the Tandori space $\widetilde{L_{1}}$ with the norm $\Vert f\Vert _{\widetilde{L_{1}}}=\Vert \widetilde{f}\Vert _{L_{1}}$ , where $\widetilde{f}(t):=\text{ess}\,\sup _{s\geqslant t}|f(s)|$ . Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.


2018 ◽  
Vol 467 (2) ◽  
pp. 1038-1065 ◽  
Author(s):  
Ihab Al Alam ◽  
Loïc Gaillard ◽  
Georges Habib ◽  
Pascal Lefèvre ◽  
Fares Maalouf

2018 ◽  
Vol 112 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Werner J. Ricker

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