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The Sandwich Rule for Sequences of Self-Adjoint Operators and Some Applications

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Abstract

In this paper, we mainly deal with sequences of bounded linear operators on Hilbert space. The main result is the so-called squeeze theorem (or sandwich rule) for convergent sequences of self-adjoint operators. We show that this theorem remains valid for all three main topologies on B(H). Some interesting consequences are given.

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Acknowledgement

The authors wish to warmly thank the referee for shortening the proof of Theorem 2.2 (cf. [2]), and for extending the conclusion of Corollary 2.6 to the case of the strong operator topology.

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Authors and Affiliations

  1. The Higher School of Exonomics, Oran, Algeria

    Ch. Chellali

  2. Laboratoire d’Analyse Mathématique et Applications, Department of Mathematics, University of Oran 1, Ahmed Ben Bella, El Menouar, B.P. 1524, Oran, 31000, Algeria

    M. H. Mortad

Authors
  1. Ch. Chellali
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  2. M. H. Mortad
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Correspondence to M. H. Mortad.

Additional information

M. H. Mortad is partially supported by “Laboratoire d’Analyse Mathématique et Applications”.

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Chellali, C., Mortad, M.H. The Sandwich Rule for Sequences of Self-Adjoint Operators and Some Applications. Anal Math 48, 991–996 (2022). https://doi.org/10.1007/s10476-022-0171-5

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  • DOI: https://doi.org/10.1007/s10476-022-0171-5

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