The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-v...The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.展开更多
A∈B（H） is called Drazin invertible if A has finite ascent and descent. Let σD （A）={λ∈ C ： A -λI is not Drazin invertible } be the Drazin .spectrum. This paper shows that if Mc =（A C 0 B）is a 2 × 2 upp...A∈B（H） is called Drazin invertible if A has finite ascent and descent. Let σD （A）={λ∈ C ： A -λI is not Drazin invertible } be the Drazin .spectrum. This paper shows that if Mc =（A C 0 B）is a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ＋ K, then the passage from OσD（A） U σD（B） to σD（Mc） is accomplished by removing certain open subsets of σD（A）∩σD（B） from the former, that is, there is equality σD（A）∪σD（B）=σD（MC）∪Gwhere G is the union of certain holes in σD （Me） which happen to be subsets of σD （A）∩σD （B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2×2 operator matrices. By using Drazin spectrum, it also explores how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2×2 upper triangular operator matrices on the Hilbert space.展开更多
In this paper, by defining two new spectral sets, we give the necessary and sufficient conditions for Browder's theorem and Weyl's theorem for bounded linear operator T and f(T), where f∈H(σ(T)) and H(σ(T))...In this paper, by defining two new spectral sets, we give the necessary and sufficient conditions for Browder's theorem and Weyl's theorem for bounded linear operator T and f(T), where f∈H(σ(T)) and H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T).展开更多
文摘The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.
基金the National Natural Science Foundation of China (10571099)
文摘A∈B（H） is called Drazin invertible if A has finite ascent and descent. Let σD （A）={λ∈ C ： A -λI is not Drazin invertible } be the Drazin .spectrum. This paper shows that if Mc =（A C 0 B）is a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ＋ K, then the passage from OσD（A） U σD（B） to σD（Mc） is accomplished by removing certain open subsets of σD（A）∩σD（B） from the former, that is, there is equality σD（A）∪σD（B）=σD（MC）∪Gwhere G is the union of certain holes in σD （Me） which happen to be subsets of σD （A）∩σD （B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2×2 operator matrices. By using Drazin spectrum, it also explores how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2×2 upper triangular operator matrices on the Hilbert space.
文摘In this paper, by defining two new spectral sets, we give the necessary and sufficient conditions for Browder's theorem and Weyl's theorem for bounded linear operator T and f(T), where f∈H(σ(T)) and H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T).
