Banach spaces which always produce octahedral spaces of operators

  1. Rueda Zoca, Abraham 1
  1. 1 Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain
Revista:
Collectanea mathematica

ISSN: 0010-0757

Año de publicación: 2024

Volumen: 75

Fascículo: 2

Páginas: 437-451

Tipo: Artículo

DOI: 10.1007/S13348-023-00394-9 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Collectanea mathematica

Resumen

We characterise those Banach spaces X which satisfy that L(Y, X) is octahedral for every non-zero Banach space Y. They are those satisfying that, for every finite dimensional subspace Z, can be finitely-representable in a part of X kind of -orthogonal to Z. We also prove that L(Y, X) is octahedral for every Y if, and only if, is octahedral for every and . Finally, we find examples of Banach spaces satisfying the above conditions like spaces with octahedral norms or -preduals with the Daugavet property.

€ Ver financiación

Información de financiación

Financiadores

Referencias bibliográficas

  • Abrahansen, T.A., Lima, V., Nygaard, O.: Remarks on diameter two properties. J. Convex Anal. 20(2), 439–452 (2013)
  • Albiac, F., Kalton, N.J.: Topics in Banach Space Theory. Springer, Berlin (2006)
  • Avilés, A., Martínez-Cervantes, G.: Complete metric spaces with property (Z) are length spaces. J. Math. Anal. Appl. 473(1), 334–344 (2019)
  • Avilés, A., Martínez-Cervantes, G., Rueda Zoca, A.: -orthogonal elements and -orthogonal sequences, to appear in Int. Math. Res. Not
  • Becerra, J., Martín, M.: The Daugavet property for Lindenstrauss spaces. In: Jesus, M.F.C., William, B.J. (eds.) Methods in Banach Space Theory. London Mathematical Society Lecture Note Series, vol. 337, pp. 91–96. (2006)
  • Becerra Guerrero, J., López-Pérez, G., Rueda Zoca, A.: Octahedral norms and convex combination of slices in Banach spaces. J. Funct. Anal. 266(4), 2424–2435 (2014)
  • Becerra Guerrero, J., López-Pérez, G., Rueda Zoca, A.: Octahedral norms in spaces of operators. J. Math. Anal. Appl. 427(1), 171–184 (2015)
  • Ciaci, S., Langemets, J., Lissitsin, A.: A characterization of Banach spaces containing via ball-covering properties, to appear in Isr. J. Math
  • Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, J., Zizler, V.: Functional Analysis and Infinite dimensional Geometry. CMS Books in Mathematics. Springer, New York (2001)
  • Godefroy, G.: Metric characterization of first Baire class linear forms and octahedral norms. Studia Math. 95(1), 1–15 (1989)
  • Godefroy, G., Kalton, N.J.: The ball topology and its applications. Contemp. Math. 85, 195–238 (1989)
  • Haller, R., Langemets, J., Nadel, R.: Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums. Banach J. Math. Anal. 12(1), 222–239 (2018)
  • Haller, R., Langemets, J., Põldvere, M.: On duality of diameter 2 properties. J. Conv. Anal. 22(2), 465–483 (2015)
  • Haller, R., Langemets, J., Põldvere, M.: Rough norms in spaces of operators. Math. Nachr. 290(11–12), 1678–1688 (2017)
  • Harmand, P., Werner, D., Werner, W.: -Ideals in Banach Spaces and Banach algebras. Lecture Notes in Mathematics, vol. 1547. Springer, Berlin (1993)
  • Hardtke, J.D.: Summands in locally almost square and locally octahedral spaces. Acta Comment. Univ. Tartu. Math. 22(1), 149–162 (2018)
  • Langemets, J., Lima, V., Rueda Zoca, A.: Octahedral norms in tensor products of Banach spaces. Q. J. Math. 68(4), 1247–1260 (2017)
  • Langemets, J., López-Pérez, G.: Bidual octahedral renormings and strong regularity in Banach spaces. J. Inst. Math. Jussieu 20(2), 569–585 (2021)
  • Langemets, J., Rueda Zoca, A.: Octahedral norms in duals and biduals of Lipschitz-free spaces. J. Funct. Anal. 279, 108557 (2020)
  • Lindenstrauss, J.: Extension of Compact Operators, vol. 48. Memoirs of the American Mathematical Society, Providence (1964)
  • López-Pérez, G., Rueda Zoca, A.: -orthogonality, octahedrality and Daugavet property in Banach spaces. Adv. Math. 383, 107719 (2021)
  • Martín, M., Rueda Zoca, A.: Daugavet property in projective symmetric tensor products of Banach spaces. Banach J. Math. Anal. 16, 35 (2022)
Fuente de los datos: Dialnet