Spectral Properties of the Operators AB and BA

Spectral Properties of the Operators AB and BA 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Notes Springer Journals

Spectral Properties of the Operators AB and BA

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Mathematics, general
ISSN
0001-4346
eISSN
1573-8876
D.O.I.
10.1134/S0001434618010212
Publisher site
See Article on Publisher Site

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.

Journal

Mathematical NotesSpringer Journals

Published: Mar 14, 2018

References

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