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On Structral Properties of Some Banach Space-Valued Schroder Sequence Spaces
(Mdpi, 2025) Yilmaz, Yilmaz; Tuncer, A. Nihal; Yalcin, Seckin
Some properties on Banach spaces, such as the Radon-Riesz, Dunford-Pettis and approximation properties, allow us to better understand the naive details about the structure of space and the robust inhomogeneities and symmetries in space. In this work we try to examine such properties of vector-valued Schroder sequence spaces. Further, we show that these sequence spaces have a kind of Schauder basis. We also prove that l(1)(S, V) possesses the Dunford-Pettis property and demonstrate that l(p)(S, V) satisfies the approximation property for 1 <= p < infinity under certain conditions and l(infinity)(S, V) has the Hahn-Banach extension property. Finally, we show that l(2)(S, V) has the Radon-Riesz property whenever V has it.