Open Access
April 2017 Extended spectrum and extended eigenspaces of quasinormal operators
Gilles Cassier, Hasan Alkanjo
Banach J. Math. Anal. 11(2): 266-281 (April 2017). DOI: 10.1215/17358787-3812451


We say that a complex number λ is an extended eigenvalue of a bounded linear operator T on a Hilbert space H if there exists a nonzero bounded linear operator X acting on H, called the extended eigenvector associated to λ, and satisfying the equation TX=λXT. In this article, we describe the sets of extended eigenvalues and extended eigenvectors for the quasinormal operators.


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Gilles Cassier. Hasan Alkanjo. "Extended spectrum and extended eigenspaces of quasinormal operators." Banach J. Math. Anal. 11 (2) 266 - 281, April 2017.


Received: 21 December 2015; Accepted: 20 April 2016; Published: April 2017
First available in Project Euclid: 14 January 2017

zbMATH: 1373.47018
MathSciNet: MR3597563
Digital Object Identifier: 10.1215/17358787-3812451

Primary: 47B20
Secondary: 47A25 , 47A60 , 47A75 , 47A80

Keywords: $\lambda$-intertwining operators , extended eigenspaces , extended eigenvalues , intertwining values , quasinormal operators

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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