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Mat. Zametki, 2018, Volume 103, Issue 2, Pages 196–209 (Mi mz11291)  

This article is cited in 1 scientific paper (total in 1 paper)

Spectral Properties of the Operators $AB$ and $BA$

D. B. Didenko

Voronezh State University

Abstract: For linear bounded operators $A$$B$ from the Banach algebra of linear bounded operators acting in a Banach space, we prove a number of statements on the coincidence of the properties of the operators $I_{Y}-AB$, $I_{X}-BA$ related to their kernels and images. In particular, we establish the identical dimension of the kernels, their simultaneous complementability property, the coincidence of the codimensions of the images, their simultaneous Fredholm property and the coincidence of their Fredholm indices. We construct projections onto the image and the kernel of these operators. We establish the simultaneous nonquasianalyticity property of the operators $AB$ and $BA$.

Keywords: linear bounded operator, reversibility states, spectrum, Fredholm property, projection operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00197
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00197.


DOI: https://doi.org/10.4213/mzm11291

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English version:
Mathematical Notes, 2018, 103:2, 196–208

Bibliographic databases:

UDC: 517.984
Received: 21.06.2016

Citation: D. B. Didenko, “Spectral Properties of the Operators $AB$ and $BA$”, Mat. Zametki, 103:2 (2018), 196–209; Math. Notes, 103:2 (2018), 196–208

Citation in format AMSBIB
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\pages 196--209
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  • http://mi.mathnet.ru/eng/mz11291
  • https://doi.org/10.4213/mzm11291
  • http://mi.mathnet.ru/eng/mz/v103/i2/p196

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Baskakov, D. B. Didenko, “Spectral Analysis of Operator Polynomials and Second-Order Differential Operators”, Math. Notes, 108:4 (2020), 477–491  mathnet  crossref  crossref
  • Математические заметки Mathematical Notes
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