Toeplitz Operators on Flows

摘要: Abstract Let R act continuously on a compact Hausdorff space X giving rise to flow , let ϑ ϵ C ( ), and T x denote the Toeplitz operator H 2 (R) determined by function defined t ) = + ). In this paper, we investigate relation between spectral properties of dynamical flow, value distribution theory ϑ. The analysis proceeds imbedding in type II ∞ factor computing real-valued index la Connes. Our sharpest invertibility result asserts that if is strictly ergodic asymptotic cycle injective 1 Z), then invertible only does not vanish determines zero element Z). This generalizes classical Gohberg Krein its extension operators with almost periodic symbols due Coburn, Douglas, Schaeffer Singer. When analytic, sense belongs for all relate density zeros upper half-plane. Much our efforts achieve are devoted generalizing arbitrary flows analytic functions developed Bohr, Jessen, Tornehave others.