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Maps Preserving Numerical Radius or Cross Norms on 2×2 Matrix Algebras

Author: ZhangWenFang
Tutor: HouJinChuan
School: Taiyuan University of Technology
Course: Applied Mathematics
Keywords: Matrix algebra Mapping Product * Product Semi - Jordan * multiplied Numerical Radius Cross - norm
CLC: O151.21
Type: Master's thesis
Year: 2010
Downloads: 25
Quote: 0
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Abstract


Operator algebra theory in the 1930s , with the rapid development of this theory , it has become a popular branch of modern mathematics it with quantum mechanics , non-commutative geometry , linear systems and control theory , number theory , as well as some of the other branch of mathematics has surprising ties and mutual penetration of operator algebra on maintaining research to maintain the operator algebra mapping characterizations of some characteristics of the same problem . norm matrix and operator of Paul numerical radius or cross characterization of nonlinear mapping problem has been extensive and in-depth research, and get a good conclusion , but so far related to the article on the numerical radius and cross norm to keep mostly assumptions Hilbert space of dimension greater than 2 dimension 2 case has not yet article to discuss the second - order matrix algebra has a basis of an important role in both theoretical and applied aspects of , for example , the second-order matrix algebra is the mathematical theory of single quantum systems framework , it is necessary the situation in the second matrix algebra answers to the above questions specializes in paper space dimension greater than 2:00 research on the basis of the fundamental theorem of quantum mechanics , that Wigner 's Theorem , the complex second-order matrix algebra on maintaining matrix multiplication radius the matrix * product of matrix semi Jordan * the value of the product or cross norm nonlinear surjective complete portrayed class mapping and classification , and thus improve the problem of the main results of this paper : ( 1 ) characterize Paul on second - order matrix algebra matrix product numerical radius or cross - norm mapping . ( 2) characterize the second-order matrix algebra preserving matrix * product numerical radius or cross - mapping of the norm . ( 3 ) characterize a second order matrix algebra Paul the matrix semi Jordan * product cross norm mapping .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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