Ideal operators and relative Godun sets

doi:10.17398/2605-5686.34.1.1

Autores/as

  • S. Dutta Professor Dutta passed away while the paper was being finalized.
  • C.R. Jayanarayanan Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India Department of Mathematics, Indian Institute of Technology Palakkad, India
  • Divya Khurana Department of Mathematics, Weizmann Institute of Science, Israel

Palabras clave:

Ideals, almost isometric ideals, strict ideals, maximal ideal operator, Godun sets, VN-subspaces

Resumen

In this paper we study ideals in Banach spaces through ideal operators. We provide characterisation of recently introduced notion of almost isometric ideal which is a version of Principle of Local Reflexivity for a subspace of a Banach space. Studying ideals through ideal operators give us better insight in to the properties of these subspaces vis-a-vis properties of the space itself. We provide a few applications of our characterisation theorem.

Descargas

Los datos de descarga aún no están disponibles.

Referencias

T. A. Abrahamsen, O. Nygaard, On λ-strict ideals in Banach spaces, Bull. Aust. Math. Soc. 83 (2) (2011), 231 – 240.

T. A. Abrahamsen, V. Lima, O. Nygaard, Almost isometric ideals in Banach spaces, Glasg. Math. J. 56 (2) (2014), 395 – 407.

P. Bandyopadhyay, S. Basu, S. Dutta, B. L. Lin, Very non- constrained subspaces of Banach spaces, Extracta Math. 18 (2) (2003), 161 – 185.

J. Bourgain, “New Classes of Lp-Spaces”, Lecture Notes in Mathematics 889, Springer Verlang, Berlin-New York, 1981.

C.-M. Cho, W. B. Johnson, A characterization of subspaces X of lp for which K(X) is an M -ideal in L(X), Proc. Amer. Math. Soc. 93 (3) (1985), 466 – 470.

M. González, A. Martı́nez-Abejón, Local duality for Banach spaces, Expo. Math. 33 (2) (2015), 135 – 183.

G. Godefroy, P. D. Saphar, Duality in spaces of operators and smooth norms on Banach spaces, Illinois J. Math. 32 (4) (1988), 672 – 695.

J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (3) (1979), 304 – 311.

G. Godefroy, N. J. Kalton, P. D. Saphar, Unconditional ideals in banach spaces, Studia Math. 104 (1) (1993), 13 – 59.

A. J. Lazar, J. Lindenstrauss, Banach spaces whose duals are L1 -spaces and their representing matrices, Acta Math. 126 (1971), 165 – 193.

E. Odell, H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing `1 , Israel J. Math. 20 (3-4) (1975), 375 – 384.

E. Oja, M. Põldvere, Principle of local reflexivity revisited, Proc. Amer. Math. Soc. 135 (4) (2007), 1081 – 1088 (electronic).

D. Werner, Recent progress on Daugavet property, Irish Math. Soc. Bull. 46 (2001), 77 – 97.

Descargas

Publicado

2019-06-01

Número

Sección

Geometry of Banach Spaces

Cómo citar

Ideal operators and relative Godun sets: doi:10.17398/2605-5686.34.1.1. (2019). Extracta Mathematicae, 34(1), 1-17. https://revista-em.unex.es/index.php/EM/article/view/2605-5686.34.1.1