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Characterizations of generalized pencils of pairs of projections

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Abstract

Let T be a bounded linear operator on a complex Hilbert space \(\mathcal {H}\). We present some necessary and sufficient conditions for T to be the generalized pencil \(P + \alpha Q +\beta PQ\) of a pair (P, Q) of projections at some point \((\alpha , \beta )\in \mathbb {C}^2\). The range and kernel relations of the generalized pencil T are studied and comments on the additional properties of some special generalized pencil are given.

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Authors and Affiliations

  1. School of Mathematics Science, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Tao Chen, Weining Lai & Chunyuan Deng

Authors
  1. Tao Chen
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  2. Weining Lai
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  3. Chunyuan Deng
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Correspondence to Chunyuan Deng.

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Communicated by Joseph Ball.

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Chen, T., Lai, W. & Deng, C. Characterizations of generalized pencils of pairs of projections. Banach J. Math. Anal. 18, 11 (2024). https://doi.org/10.1007/s43037-023-00322-w

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