共查询到20条相似文献,搜索用时 15 毫秒
1.
Let Mn be the algebra of n×n matrices over an algebraically closed field of characteristic zero. Let f(x) be a polynomial over with at least two distinct roots. Then all nonsingular linear maps L:Mn→Mn that map matrix roots of F(x)=0 into matrix roots of f(x}=0 are found. 相似文献
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L. Zhao 《Journal of Mathematical Analysis and Applications》2006,314(2):689-700
Let Φ:A→B be an additive surjective map between some operator algebras such that AB+BA=0 implies Φ(A)Φ(B)+Φ(B)Φ(A)=0. We show that, under some mild conditions, Φ is a Jordan homomorphism multiplied by a central element. Such operator algebras include von Neumann algebras, C∗-algebras and standard operator algebras, etc. Particularly, if H and K are infinite-dimensional (real or complex) Hilbert spaces and A=B(H) and B=B(K), then there exists a nonzero scalar c and an invertible linear or conjugate-linear operator U:H→K such that either Φ(A)=cUAU−1 for all A∈B(H), or Φ(A)=cUA∗U−1 for all A∈B(H). 相似文献
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Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B(X). A map Φ :A →A is said to be strong 3-commutativity preserving if [Φ(A), Φ(B)]3 = [A,B]3 for all A,B∈ A, where[A,B]3 is the 3-commutator of A,B defined by[A, B]3 = [[[A, B],B],B] with [A,B] = AB-BA. The main result in this paper is shown that.,if Φ is a surjective map on A, then Φ is strong 3-commutativity preserving if and only if there exist a functional h : A →F and a scalar λ∈ F with λ~4 = 1 such that Φ(A)=λ A+h(A)I for all A ∈ A. 相似文献
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Let and be standard operator algebras on infinite dimensional complex Banach spaces X and Y, respectively, and let Φ be a unital additive surjection from onto . We introduce thirteen parts of the spectrum for elements in and , and prove that if Φ preserves any one of these parts of the spectrum, then it is either an isomorphism or an anti-isomorphism. 相似文献
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In this article, we give a thorough discussion of additive maps between nest algebras acting on Banach spaces which preserve rank-one operators in both directions. 相似文献
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JinChuanHOU PeterSEMRL 《数学学报(英文版)》2003,19(3):473-484
We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrumpreserving elementary operators. Several open problems are also mentioned. 相似文献
9.
Jung-Hui Liu 《Journal of Mathematical Analysis and Applications》2006,321(2):741-750
A not necessarily continuous, linear or multiplicative function θ from an algebra A into itself is called a 2-local automorphism if θ agrees with an automorphism of A at each pair of points in A. In this paper, we study when a 2-local automorphism of a C∗-algebra, or a standard operator algebra on a locally convex space, is an automorphism. 相似文献
10.
Mostafa Mbekhta 《Proceedings of the American Mathematical Society》2007,135(11):3613-3619
Let be an infinite-dimensional separable complex Hilbert space and the algebra of all bounded linear operators on . In this paper we characterize surjective linear maps preserving the set of Fredholm operators in both directions. As an application we prove that preserves the essential spectrum if and only if the ideal of all compact operators is invariant under and the induced linear map on the Calkin algebra is either an automorphism, or an anti-automorphism. Moreover, we have, either or for every Fredholm operator .
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We describe all linear self-mappings of the space of bounded linear operators in an infinite dimensional separable complex Hilbert space which preserve the isomorphism class of the lattice of invariant operator ranges. 相似文献
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Completely rank nonincreasing linear maps on nest algebras 总被引:1,自引:0,他引:1
In this paper, the completely rank nonincreasing bounded linear maps on nest algebras acting on separable Hilbert spaces are characterized, and an affirmative answer to a problem posed by Hadwin and Larson is given for the case of such nest algebras.
13.
Douglas R. Farenick 《Proceedings of the American Mathematical Society》1996,124(11):3381-3390
Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible positive linear maps on von Neumann algebras are explicitly constructed, and a criterion for the irreducibility of decomposable positive maps on full matrix algebras is given.
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Let A be a unital C*-algebra of real rank zero and B be a unital semisimple complex Banach algebra. We characterize linear maps from A onto B preserving different essential spectral sets and quantities such as the essential spectrum, the (left, right) essential spectrum, the Weyl spectrum, the index and the essential spectral radius. 相似文献
15.
We characterize the surjective additive maps compressing the spectral function Δ(·) between standard operator algebras acting on complex Banach spaces, where Δ(·) stands for any one of nine spectral functions σ(·), σl(·), σr(·),σl(·) ∩ σr(·), δσ(·), ησ(·), σap(·), σs(·), and σap(·) ∩ σs(·). 相似文献
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Yiqiu Du 《Linear and Multilinear Algebra》2013,61(8):933-940
The aim of this article is to prove a result on the additivity of Jordan maps on triangular algebras. As a consequence the additivity of Jordan maps on upper triangular matrix algebras over a faithful commutative ring of 2-torsion free is determined. 相似文献
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Pengtong Li 《Journal of Mathematical Analysis and Applications》2006,320(1):174-191
Let A1, A2 be algebras and let M:A1→A2, M∗:A2→A1 be maps. An elementary map of A1×A2 is an ordered pair (M,M∗) such that
20.
Xiaofei Qi 《Linear and Multilinear Algebra》2013,61(4):391-397
Let 𝒜 and ? be unital algebras over a commutative ring ?, and ? be a (𝒜,??)-bimodule, which is faithful as a left 𝒜-module and also as a right ?-module. Let 𝒰?=?Tri(𝒜,??,??) be the triangular algebra and 𝒱 any algebra over ?. Assume that Φ?:?𝒰?→?𝒱 is a Lie multiplicative isomorphism, that is, Φ satisfies Φ(ST???TS)?=?Φ(S)Φ(T)???Φ(T)Φ(S) for all S, T?∈?𝒰. Then Φ(S?+?T)?=?Φ(S)?+?Φ(T)?+?Z S,T for all S, T?∈?𝒰, where Z S,T is an element in the centre 𝒵(𝒱) of 𝒱 depending on S and T. 相似文献