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Davis–Wielandt shells of semi-Hilbertian space operators and its applications

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Abstract

In this paper we generalize the concept of Davis–Wielandt shell of operators on a Hilbert space when a semi-inner product induced by a positive operator A is considered. Moreover, we investigate the parallelism of A-bounded operators with respect to the seminorm and the numerical radius induced by A. Mainly, we characterize A-normaloid operators in terms of their A-Davis–Wielandt radii. In addition, a connection between A-seminorm-parallelism to the identity operator and an equality condition for the A-Davis–Wielandt radius is proved. This generalizes the well-known results in Chan and Chan (Oper Matrices 11(3):885–890, 2017), Zamani et al. (Linear Multilinear Algebra 67(11):2147–2158, 2019). Some other related results are also discussed.

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Authors and Affiliations

  1. University of Sfax, Sfax, Tunisia

    Kais Feki

  2. Mathematical Analysis and Applications, Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia

    Sid Ahmed Ould Ahmed Mahmoud

Authors
  1. Kais Feki
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  2. Sid Ahmed Ould Ahmed Mahmoud
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Correspondence to Kais Feki.

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Communicated by Fuad Kittaneh.

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Feki, K., Ahmed Mahmoud, S.A.O. Davis–Wielandt shells of semi-Hilbertian space operators and its applications. Banach J. Math. Anal. 14, 1281–1304 (2020). https://doi.org/10.1007/s43037-020-00063-0

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  • DOI: https://doi.org/10.1007/s43037-020-00063-0

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