Linear operators preserving unitarily invariant norms of matrices |
| |
Authors: | Chi-Kwong Li Nam-Kiu Tsing |
| |
Institution: |
a Department of Mathematics, The college of william and Mary, Williamsburg, Virginia
b Systems Research Center and Electrical Engineering Department, University of Maryland, College Park, Maryland |
| |
Abstract: | Let Fm × n be the set of all m × n matrices over the field F = C or R Denote by Un(F) the group of all n × n unitary or orthogonal matrices according as F = C or F-R. A norm N() on Fm ×n, is unitarily invariant if N(UAV) = N(A): for all A ∈ F m×n U ∈ Um(F). and V ∈ Un(F). We characterize those linear operators TFm × n → Fm × nwhich satisfy N (T(A)) = N(A)for all A ∈ Fm × n
for a given unitarily invariant norm N(). It is shown that the problem is equivalent to characterizing those operators which preserve certain subsets in Fm × n To develop the theory we prove some results concerning unitary operators on Fm × n which are of independent interest. |
| |
Keywords: | |
本文献已被 InformaWorld 等数据库收录! |
|