[PDF][PDF] On Cones Associated with Schauder Frames

S Jahan, V Kumar - Jordan Journal of Mathematics and Statistics …, 2017 - journals.yu.edu.jo
Jordan Journal of Mathematics and Statistics (JJMS), 2017journals.yu.edu.jo
In this paper, we define cone CF associated with Schauder frame F=({xn},{fn}) in Banach
spaces. A necessary and sufficient condition for a cone CF to be normal has been given.
Also, we have obtained a sufficient condition for the cone CF to be minihedral and show that
the converse is not true in general. Moreover, we have given some necessary and sufficient
conditions for the cone CF to be generating and has a bounded base. Finally, a
characterization of normalized Schauder frames of type P∗, al+ and w0 and a sufficient …
Abstract
In this paper, we define cone CF associated with Schauder frame F=({xn},{fn}) in Banach spaces. A necessary and sufficient condition for a cone CF to be normal has been given. Also, we have obtained a sufficient condition for the cone CF to be minihedral and show that the converse is not true in general. Moreover, we have given some necessary and sufficient conditions for the cone CF to be generating and has a bounded base. Finally, a characterization of normalized Schauder frames of type P∗, al+ and w0 and a sufficient condition for the cone CF1 associated with normalized shrinking Schauder frame F1={(enxn, enfn)} has been given.
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