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

YILMAZ Y., TUNCER A. N., YALÇIN S.

Symmetry, cilt.17, sa.7, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 7
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17070977
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Approximation property, Dunford-Pettis property, Radon-Riesz Property, Schröder sequence spaces, vector-valued sequence spaces
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.