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<p>The purpose of this paper is to initiate the study of the classes of essentially left and essentially right Drazin-invertible multivalued linear operators on Banach spaces. It is shown, among other results, that these multivalued operators can be completely characterized in terms of a direct sum decomposition consisting of a left (right) Fredholm multivalued operator and a bounded nilpotent operator. As a consequence of these decompositions, many other characterizations of these multivalued operators are obtained. More precisely, we provide another type of decomposition for essentially left and essentially right Drazin-invertible multivalued operators via the new notion of normal decomposability, and we also characterize them using restrictions and projections. We then show the connection between these multivalued operators and B-Fredholm multivalued operators. The results obtained in this study generalize and enhance certain characterizations previously established in [<CitationRef CitationID="CR36">36</CitationRef>] in operator theory. As an application, we investigate the Drazin invertibility of block linear relation matrices. More specifically, we apply the obtained results to study linear differential inclusions.</p>

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One-sided essentially Drazin-invertible multivalued linear operators

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Ayoub Ghorbel,
  • Melik Lajnef

摘要

The purpose of this paper is to initiate the study of the classes of essentially left and essentially right Drazin-invertible multivalued linear operators on Banach spaces. It is shown, among other results, that these multivalued operators can be completely characterized in terms of a direct sum decomposition consisting of a left (right) Fredholm multivalued operator and a bounded nilpotent operator. As a consequence of these decompositions, many other characterizations of these multivalued operators are obtained. More precisely, we provide another type of decomposition for essentially left and essentially right Drazin-invertible multivalued operators via the new notion of normal decomposability, and we also characterize them using restrictions and projections. We then show the connection between these multivalued operators and B-Fredholm multivalued operators. The results obtained in this study generalize and enhance certain characterizations previously established in [36] in operator theory. As an application, we investigate the Drazin invertibility of block linear relation matrices. More specifically, we apply the obtained results to study linear differential inclusions.