I. F. Z. Bensaid, F. León-Saavedra, P. Romero de la Rosa
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引用次数: 0
Abstract
Let \(\alpha\) be a complex scalar, and let \(A\) be a bounded linear operator on a Hilbert space \(H\). We say that \(\alpha\) is an extended eigenvalue of \(A\) if there exists a nonzero bounded linear operator \(X\) such that \(AX=\alpha XA\). In weighted Hardy spaces invariant under automorphisms, we completely compute the extended eigenvalues of composition operators induced by linear fractional self-mappings of the unit disk \(\mathbb{D}\) with one fixed point in \(\mathbb{D}\) and one outside \(\overline{\mathbb{D}}\). Such classes of transformations include elliptic and loxodromic mappings as well as a hyperbolic nonautomorphic mapping.
期刊介绍:
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.