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Let A be a standard operator algebra on a complex Hilbert space H of dimension greater than 2. By invariants of certain functional values of operator products, we characterize some surjective maps on A. Furthermore, several kinds of general preserver problems on standard operator algebras are solved when we take respectively the functional as, for example, k-numerical radius (k?1), operator norm, Ky Fan k-norm, Schatten p-norm (1?p<∞), and so on. 相似文献
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笔者最近有机会听了一些老师的初中物理课,在一些老师的“内能”概念教学实践中,笔者发现他们总是在想方设法运用各种教学手段强调如下两个教学要点: 相似文献
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In this article, we define and study the Gorenstein flat dimension and Gorenstein cotorsion dimension for unbounded complexes over GF-closed rings by constructions of resolutions of unbounded complexes. The behavior of the dimensions under change of rings is investigated. 相似文献
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Let H be an infinite-dimensional complex Hilbert space and (H)the algebra of all bounded linear operators on H. Some characterizationsare obtained of linear maps on (H) preserving essential spectralfunctions such as the intersection of left essential spectrumand right essential spectrum of operators, preserving Fredholmoperators, and preserving semi-Fredholm operators, and preservingcloseness of operator ranges. A result of Mbekhta, Rodman andemrl (Integral Equations Operator Theory 55 (2006) 93-109) ongeneralized invertibility preserving linear maps is improved. 相似文献
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CUI Jianlian & HOU Jinchuan Department of Mathematical Science Tsinghua University Beijing China Department of Applied Mathematics Taiyuan University of Technology Taiyuan China Department of Mathematics Shanxi Teachers University Linfen China 《中国科学A辑(英文版)》2005,(12)
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
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Let H be an infinite dimensional complex Hilbert space. Denote by B(H)the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that φ is a surjective map from B(H) onto itself. If for everyλ∈ {-1, 1, 2, 3, 1/2, 1/3} and A, B ∈ B(H), A - λB ∈ I(H) (→)φ(A) - λφ(B) ∈ I(H), then φis a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that φ(A) = TAT-1 for all A ∈ B(H), or φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A - iB ∈ I(H) (→)φ(A) - iφ(B) ∈ I(H), here i is the imaginary unit, then φ is either an automorphism or an anti-automorphism. 相似文献
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对 于 具 有 离 散 谱 的 正 算 子 A, B, 我 们 给 出 了 一 个 闭 集 成 为 2 × 2 缺 项 算 子 矩 阵 A ?? B 的某个正 补的谱的一些 判别条件 相似文献
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Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras 总被引:1,自引:0,他引:1
A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(T−S))=w(T−S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let and be two atomic nests on complex Hilbert spaces H and K, respectively. Denote the nest algebra associated with and the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometries from onto and a thorough classification of numerical radius isometries from onto . 相似文献