On Structral Properties of Some Banach Space-Valued Schröder Sequence Spaces

YILMAZ Y., TUNCER A. N., YALÇIN S.

Symmetry, vol.17, no.7, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 7
  • Publication Date: 2025
  • Doi Number: 10.3390/sym17070977
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Approximation property, Dunford-Pettis property, Radon-Riesz Property, Schröder sequence spaces, vector-valued sequence spaces
  • Inonu University Affiliated: Yes

Abstract

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 Schröder sequence spaces. Further, we show that these sequence spaces have a kind of Schauder basis. We also prove that (Formula presented.) possesses the Dunford–Pettis property and demonstrate that (Formula presented.) satisfies the approximation property for (Formula presented.) under certain conditions and (Formula presented.) has the Hahn–Banach extension property. Finally, we show that (Formula presented.) has the Radon–Riesz property whenever V has it.