Linear maps preserving the spectral radius

被引：82
作者：
Bresar, M
Semrl, P
机构：
[1] University of Maribor, PF, 62000 Maribor
[2] University of Maribor, TF, 62000 Maribor
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 1996年 / 142卷 / 02期
关键词：
D O I：
10.1006/jfan.1996.0153
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let X be a complex Banach space. If Phi: B(X) --> B(X) is a surjective linear map such that A and Phi(A) have the same spectral radius for every A is an element of B(X), then Phi = c Theta where Theta is either an algebra-automorphism or antiautomorphism of B(X) and c is complex constant such that /c/ = 1. (C) 1996 Academic Press, Inc.
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页码：360 / 368
页数：9
相关论文
共 12 条
  • [1] THE UNIQUENESS OF THE COMPLETE NORM TOPOLOGY IN BANACH-ALGEBRAS AND BANACH JORDAN ALGEBRAS
    AUPETIT, B
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1982, 47 (01) : 1 - 6
  • [2] SPECTRUM PRESERVING LINEAR MAPPING SIN BANACH-ALGEBRAS
    AUPETIT, B
    MOUTON, HDT
    [J]. STUDIA MATHEMATICA, 1994, 109 (01) : 91 - 100
  • [3] Aupetit B., 1979, Lecture Notes in Math., V735
  • [4] LINEAR TRANSFORMATIONS THAT PRESERVE THE NILPOTENT MATRICES
    BOTTA, P
    PIERCE, S
    WATKINS, W
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 1983, 104 (01) : 39 - 46
  • [5] FILLMORE PA, 1967, ACTA SCI MATH, V28, P285
  • [6] SPECTRUM-PRESERVING LINEAR-MAPS
    JAFARIAN, AA
    SOUROUR, AR
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1986, 66 (02) : 255 - 261
  • [7] Kaplansky I., 1970, REGIONAL C SERIES MA, V1
  • [8] Marcus M., 1959, Can. J. Math., V11, P61
  • [9] Mityagin B.S., 1970, Funkc. Anal. Prilozh., V4, P61
  • [10] PEARCY C, 1967, MICH MATH J, V14, P453
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