<p style='text-indent:20px;'>We develop a random version of the perturbation theory Gouëzel, Keller, and Liverani, consequently obtain results on stability Oseledets splittings Lyapunov exponents for operator cocycles. By applying to Perron-Frobenius cocycles associated <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{C}^k $\end{document}</tex-math></inlin...

We show that the symbol of a bounded composition operator on Wiener algebra Dirichlet series does not need to belong this algebra. Our example even gives an absolutely summing (hence compact) operator.

We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.

We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.

The object of this present paper is to study Toeplitz operators and Hankel operators on the Hardy space of the unit sphere S in C through the generalized area integral of harmonic functions on the unit ball B in C. In particular we consider the question of when the product of two Toeplitz operators is a compact perturbation of a Toeplitz operator. It follows from a theorem in [DJ] that T,T can ...

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

LetM be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n×n real skew-symmetric matrices θ. TheMθ’s together with the canonical Dirac operator (D,H) on M are an isospectral deformation of M . The Dirac operator D defines a Lipschitz seminorm on C(Mθ), which defines a metric on the state space of C(Mθ). We show th...