Geodesic
Note on the spectral theorem for unbounded non-selfadjoint operators
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 42-61

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In this paper, we deal with non-selfadjoint operators with the compact resolvent. Having been inspired by the Lidskii idea involving a notion of convergence of a series on the root vectors of the operator in a weaker – Abel-Lidskii sense, we proceed constructing theory in the direction. The main concept of the paper is a generalization of the spectral theorem for a non-selfadjoint operator. In this way, we come to the definition of the operator function of an unbounded non-selfadjoint operator. As an application, we notice some approaches allowing us to principally broaden conditions imposed on the right-hand side of the evolution equation in the abstract Hilbert space.
Keywords: Spectral theorem, Abel-Lidskii basis property, Schatten-von Neumann class, operator function
Mots-clés : evolution equation. 
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     author = {M. V. Kukushkin},
     title = {Note on the spectral theorem for unbounded non-selfadjoint operators},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a3/}
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M. V. Kukushkin. Note on the spectral theorem for unbounded non-selfadjoint operators. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 42-61. http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a3/