保持拟可逆性或拟零因子的可加映射
Additive Maps Preserving Quasi-invertibilities or Quasi-zero Divisors
设X和Y是维数大于1的复Banach空间,A和B分别是B(X)和B(Y)中包含有限秩算子的范数闭子代数.∀A,B∈A,定义AB=A+B-AB,称为A,B的拟积.刻画了从A到B的双边保持算子的(左,右)拟可逆性或(左,右,半)拟零因子的可加满射的结构.
Let X, Y be complex Banach spaces with dimentions greater than 1. Let A, B be normed closed subalgebras of B(X), B(Y) containing finite rank operators, respectively. For any A, B∈A, we define the quasi-product of A and B as AB=A+B-AB. In this paper, A characterization of additive mappings from A onto B which preserve any one of (left, right) quasi-invertibility and (left, right, semi) quasizero divisors in both directions is given.
算子代数 / 拟可逆性 / 拟零因子 / 同构 {{custom_keyword}} /
operator algebras / quasi-invertibility / quasi-zero divisors / isomorphisms {{custom_keyword}} /
[1] Amberg B., Sysak Y. P., Associative rings whose adjoint semigroup is locally nilpotent, Archiv Math., 2001, 76(6):426-435.
[2] Amberg B., Sysak Y. P., Radical rings with Engel conditions, J. Algebra, 2000, 231(1):364-373.
[3] Aupetit B., Spectrum-preserving linear mappings between Banach algebras or Jordan Banach algebras, J. London Math. Soc., 2002, 62(3):917-924.
[4] Chahbi A., Charifi A., Kabbaj S., Linear maps preserving quasi-unitary operators, Gen. Math. Notes, 2014, 21(1):1-9.
[5] Choi M. D., Hadwin D., On positive linear maps preserving invertibility, J. Funct. Anal., 1984, 59(3):462-469.
[6] Hille E., Phillips R. S., Functional Analysis and Semi-Groups, Providence, Rhode Island:Amer. Math. Soc., 1957:680-694.
[7] Hou J., Cui J., Additive maps on standard operator algebras preserving invertibilities or zero divisors, Linear Algebra Appl., 2003, 359(1-3):219-233.
[8] Hou J., Cui J., Introduction to the Linear Maps on Operator Algebras (in Chinese), Science Press, Beijing, 2002.
[9] Jacobson N., The radical and semi-simplicity for arbitrary rings, Amer. J. Math., 1945, 67(2):300-320.
[10] Kaplansky I., Algebraic and Analytic Aspects of Operator Algebras.1, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, 1970.
[11] Kaplansky I., Topological rings, Amer. J. Math., 1947, 69(1):153-183.
[12] Krasil'nikov A. N., On the semigroup and Lie nilpotency of associative algebras, Mat. Zametki, 1997, 62(4):510-519(Translated in:Math. Notes, 1997, 62(4):426-433).
[13] Omladic M., Šemrl P., Additive mapping preserving operators of rank one, Linear Algebra Appl., 1993, 182(15):239-256.
[14] Omladic M., Šemrl P., Spectrum-preserving additive maps, Linear Algebra Appl., 1991, 153:67-72.
[15] Qi X., Hou J., Deng J., Lie ring isomorphisms between nest algebras on Banach spaces, J. Funct. Anal., 2014, 266(7):4266-4292.
[16] Sourour A. R., Invertibility preserving linear maps on L(X), Trans. Amer. Math. Soc., 1996, 348:13-30.
[17] Wang Y., Ji G., Quasi-automorphisms on B(X) (in Chinese), Adv. Math., 2016, 45(1):111-116.
[18] Wang M., Ji G., A characterization of *-isomorphism on factor von Neumann algebras (in Chinese), Acta Math. Sinica, 2015, 58(1):71-78.
国家自然科学基金资助项目(11371233);中央高校基本科研业务费专项资金(GK201301007)
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