关于一类广义导算子

A Kind of Generalized Derivations

本文研究广义导算子(其中T_φ,T_ψ是Toeplitz算子)的谱σ(△_(φψ))的结构及△_(φψ)(S)与S的性质的关联。

△_(ρψ) denotes the generalized derivations on L(H^2(D)): △_(ρψ)(x)= T_ρX-XT_ρ(X∈ L(H^2(D))). In this article we show that σ(△_(ρψ)), σ_c(△_(ρψ))are connected and discuss the geometrical structures of the spectra and essential spectra of △_(ρψ), with ρ, ψ satisfying certain conditions. Under the assumption ρ, ψ∈C (D), S∈T (L~∞(D)) we discuss the relationships between △_(ρψ)(S) and S (regarding Fredholmness, essential spectra, etc.)