映射Fp:X→‖AXB-C‖pp的临界点的特征

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映射F_p:X→‖AXB-C‖_p^p的临界点的特征

基金项目: 河南省教委基金;(98110012)

Department of Mathematics, Heran Normal University, Xinxiang, He'nan 45002, P R China

摘要: 对于Hilbert空间上有界线性算子A、B、C,考虑了当A有一个广义逆A^-使得(AA^-)^*=AA^-,B有一个广义逆B^-使得(B^-B)^*= B^-B时,映射 F_p:X→‖AXB-C‖_p^p临界点的特征的一般形式(1<p<∞),推广了P.J.Mahar的关于对p=2时的结果,并指出该定理可推广到多个算子的情形。
- 广义逆 /
- 临界点 /
- 极分解
Abstract: Suppose A,B and C are the bounded linear operators on a Hilbert space H,when A has a generalized inverse A^- such that (AA^-)^*＝AA^- and B has a generalized inverse B^- such that (B^-B)^*＝B^-B, the general characteristic forms for the critical points of the map F_p:X→‖AXB-C‖_p^p(1<p<∞),have been obtained,it is a generalization for P.J.Maher result about p=2.Similarly,the same question has been discussed for several operators.
- generalized inverse /
- critical point /
- polar decomposition

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