On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space

  1. Bhunia, Pintu 1
  2. Paul, Kallol 1
  3. Sain, Debmalya 2
  1. 1 Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India
  2. 2 Department of Mathematics, Indian Institute of Science, Bengaluru, Karnataka, 560012, India
Revista:
Collectanea mathematica

ISSN: 0010-0757

Año de publicación: 2022

Volumen: 73

Fascículo: 3

Páginas: 521-533

Tipo: Artículo

DOI: 10.1007/S13348-021-00332-7 DIALNET GOOGLE SCHOLAR

Otras publicaciones en: Collectanea mathematica

Resumen

We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space X. We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on L(X) which is equivalent to the usual operator norm on L(X). We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral finite-dimensional Banach space.

Fuente de los datos: Dialnet