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

• Bhunia, Pintu ^[1] ; Paul, Kallol ^[1] ; Sain, Debmalya ^[2]
  1. [1] Jadavpur University

     Jadavpur University

     India

     
  2. [2] Department of Mathematics, Indian Institute of Science, Bengaluru, Karnataka, 560012, India
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 3, 2022, págs. 521-533
• Idioma: inglés
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• 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.