EXTENDED SPECTRUM AND EXTENDED EIGENSPACES OF QUASI-NORMAL OPERATORS
2017
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 extended eigen-
vector associated to λ, and satisfying the equation T X = λXT . In this
paper we describe the sets of extended eigenvalues and extended eigen-
vectors for the product of a positive and a self-adjoint operator which
are both injective. We also treat the case of normal operators.
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