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<p>In this paper, we will consider two notions of an invariant subspace for a linear relation: the first one is through the graph of a linear relation, and the second one is by using the resolvent function of a linear relation. Through some examples and preliminary results, it is shown that the second notion is more suitable when the spectral properties of liner relations are involved. In the second part of the paper, such a notion of an invariant subspace is allowed to develop, in a constructive way, the concept of group inverse for linear relations.</p>

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Restrictions of linear relations on invariant subspaces and group inverse

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  • 出版模式：

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  • 发表日期：

    2025年6月25日

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  • S. V. Djordjević,
  • I. Roque

摘要

In this paper, we will consider two notions of an invariant subspace for a linear relation: the first one is through the graph of a linear relation, and the second one is by using the resolvent function of a linear relation. Through some examples and preliminary results, it is shown that the second notion is more suitable when the spectral properties of liner relations are involved. In the second part of the paper, such a notion of an invariant subspace is allowed to develop, in a constructive way, the concept of group inverse for linear relations.