Operators with Singularcontinuous Spectrum , Vii

Self-commutators of composition operators with monomial symbols on the Bergman space

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

Spectrum and essential spectrum of linear combinations of composition operators on the Hardy space H2

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Operators with Singular Continuous Spectrum, VII. Examples with Borderline Time Decay

2 Abstract: We construct one-dimensional potentials V(x) so that if H = — JJT -fV(x) on L(IR), then H has purely singular spectrum; but for a dense set D, φ e D implies that \(φ,e~φ)\ ^ Q, | f |~ 1 / 2 ln( | f | ) for |ί| > 2. This implies the spectral measures have Hausdorff dimension one and also, following an idea of MalozemovMolchanov, provides counterexamples to the direct extension of the...

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.