保持算子乘积谱函数的映射

设A和B为无限维复Banach空间上的标准算子代数,记ΔR(·)为下列谱函数之一σR(·),σRl(·),σRr(·),σRl(·)∩σRr(·),(a)σR(·),ησR(·),σRp(·),σRc(·),σRap(·),σRs(·),σRap(·)∩σRs(·),σRp(·)∩σRc(·),σRp(·)∪σRc(·),其中R=A或B.证明了A和B之间的每个保持算子Jordan三乘积(算子乘积)之谱函数ΔR(·)的满射φ必有形式φ=επ,其中ε是1的立方根(1的平方根)而π或者是A和B之间的代数同构,或者是代数反同构.也获得不定度规空间上的标准算子代数之间保持算子斜乘积之谱函数的映射的完全刻画.     

保持算子乘积投影的线性映射

设B(H)是复Hilbert空间H上的有界线性算子全体且dim H≥2.本文证明了B(H)上的线性满射φ保持两个算子乘积非零投影性的充分必要条件是存在B(H)中的酉算子U以及复常数λ满足λ~2=1,使得φ(X)=λU~*XU,(?)X∈B(H).同时也得到了线性映射保持两个算子Jordan三乘积非零投影的充分必要条件.     

算子代数上的Jordan初等映射(英文)

给定两个环R,R’.对于满足一定条件的环R,本文证明了若M:R→R’,M*:R’→R为满射且对A,C∈R和B,D∈R’满足M（AM*（B）C+CM*（B）A）=M（A）BM（C）+M（C）BM（A）,M*（BM（A）D+DM（A）B）=M*（B）AM*（D）+M*（D）AM*（B）则M和M*是可加的;若R和R’分别包含单位I和I’,M（I）,M*（I’）可逆,则存在环同构N使得M（A）=N（A）M（I）,M*（B）=N^-1（BM（I））.特别地,若R=R’为标准算子代数或Hilbert空间套代数,则M和M*可加且存在有界可逆的线性或共轭线性算子S和T使得M（A）=SAT,M*（B）=TBS或M（A）=TA*S,M*（B）=（SBT）*对任意的A,B∈R成立.     

保持谱半径的乘法映射

设X和Y为无限维Banach空间,Φ：B（X）→B（Y）是保持谱半径的满射,且秩为1算子,则Φ具有形式Φ（T）=ATA∧-1,这里A：X→Y或是线性拓扑同构映射或是线性拓扑同构映射的共轭。     

正则Cosine算子函数的乘积扰动定理

本文研究了正则cosine算子函数的乘积扰动性,在正则化算子C的值域不 一定稠密的一般情形下,获得了若干正则cosine算子函数的乘积扰动定理.     

C－余弦算子函数的谱

Let A be the generator of a C-cosine operator functions C(t) on a Banach space X .The spectrum characterization of (unbounded) cosine operator function C(t)C^-1 on R(C²) is derived. In particular， we characterize the spectrum of strongly continuous cosine operator on a Banach space.     

Wigner定理在保持算子乘积范数正映射的应用

把Wigner定理应用于算子代数上的保持映射问题,证明了如果φ是标准算子代数上的正映射,且保持两个算子乘积的范数或奇异值的和,则φ必定具有形式φ(A)=UAU*,其中U是一个酉算子或反酉算子.     

一类本性谱有界算子的刻画

设H是一个无限维复Hilbert空间,B(H)表示H上的有界线性算子的全体,并且Φ是从B(H)到自身的线性满射.我们证明了映射Φ是本性谱有界且模紧算子的充分必要条件是Φ(K(H))■K(H)且诱导映射Φ是Calkin代数上的连续同态或连续反同态.     

标准算子代数上完全保对合性的可加映射

刻画了无限维实或复Banach空间上的标准算子代数间完全保对合性的可加映射,证明了这样的映射是同构的常数倍或(复情形下)共轭同构的常数倍.     

Linear Maps Preserving Idempotence on Nest Algebras

In this paper, we discuss the rank-l-preserving linear maps on nest algebras of Hilbertspace operators. We obtain several characterizations of such linear maps and apply them to show that a weakly continuous linear hijection on an atomic nest algebra is idempotent preserving if and only if it is a Jordan homomorphism, and in turn, if and only if it is an automorphism or an anti-automorphism.     

Maps preserving numerical ranges of operator products

Let be a complex Hilbert space, the algebra of all bounded linear operators on and the real linear space of all self-adjoint operators on . We characterize the surjective maps on or that preserve the numerical ranges of products or Jordan triple-products of operators.

     

Additive Maps Preserving Nilpotent Operators or Spectral Radius

Let X be a （real or complex） Banach space with dimension greater than 2 and let B0（X） be the subspace of B（X） spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0（X） which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф（T） = cATA^-1 or Ф（T） = cAT＇A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T＇ denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B（X） preserving spectral radius has a similar form to the above with ｜c｜ = 1.     

Local Jordan -Derivations of Standard Operator Algebras

We prove that on standard operator algebras every local Jordan -derivation is a Jordan -derivation.

     

自伴算子空间上保持Jordan积投影的线性映射

Let Bs(H) be the real linear space of all self-adjoint operators on a complex Hilbert space H with dim H ≥ 2.It is proved that a linear surjective map on Bs (H) preserves the nonzero projections of Jordan products of two operators if and only if there is a unitary or an anti-unitary operator U on H such that (X)=λU XU,X∈Bs(H) for some constant λ with λ∈{1,1}.     

Simplicity of a Vertex Operator Algebra Whose Griess Algebra is the Jordan Algebra of Symmetric Matrices

Let r ∈ ? be a complex number, and d ∈ ?_≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [4 Ashihara , T. , Miyamoto , M. ( 2009 ). Deformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras . Journal of Algebra 32 : 1593 – 1599 . [Google Scholar]] introduced a vertex operator algebra V _𝒥 of central charge dr, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size d. In this article, we prove that the vertex operator algebra V _𝒥 is simple if and only if r is not an integer. Further, in the case that r is an integer (i.e., V _𝒥 is not simple), we give a generator system of the maximal proper ideal I _r of the VOA V _𝒥 explicitly.