算子广义正交问题的研究
Study on the Generalized Orthogonal Problem of Operators
摘要: 本文研究考虑了在算子空间中矩阵作为算子的广义正交性，给出矩阵正交与迹之间的关系，并讨论了算子空间为内积空间的等价条件。
Abstract:
In this paper, the generalized orthogonality of matrix as an operator in operator space is considered, the relationship between matrix orthogonality and trace is given, and the equivalent condition that operator space is inner product space is discussed.
参考文献
|
[1]
|
Birkhoff, G. (1935) Orthogonality in Linear Metric Spaces. Duke Mathematical Journal, 1, 169-172. [Google Scholar] [CrossRef]
|
|
[2]
|
James, R.C. (1945) Orthogonality in Normed Linear Spaces. Duke Mathematical Journal, 12, 291-302. [Google Scholar] [CrossRef]
|
|
[3]
|
Bhatia, R. (1997) Matrix Analysis. Springer, New York.
|
|
[4]
|
Horn, R.A. and Johnson, C.R. (2013) Matrix Analysis. 2nd Edition, Cambridge University Press, New York.
|
|
[5]
|
Zalar, B. (1995) Jordan-Von Neumann Theorem for Saworotnow’s Generalized Hilbert Space. Acta Mathematica Hungarica, 69, 301-325. [Google Scholar] [CrossRef]
|