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On the Spectrum of the Product of Closed Operators

✍ Scribed by Volker Hardt; Alexei Konstantinov; Reinhard Mennicken

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
169 KB
Volume
215
Category
Article
ISSN
0025-584X

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✦ Synopsis

In this note we study the connection between the spectra of the products AB and BA of unbounded closed operators A and B acting in Banach spaces. Under the condition that the resolvent sets of these products are not empty we show that the spectra of AB and BA coincide away from zero and prove the commutation relation

Further, we prove statements concerning the relationship between the spectra of the operator AB and the block operator matrix 0 A B 0 .

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