Surjective Lp-isometries on Grassmann spaces
Surjective Lp-isometries on Grassmann spaces
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DOI：
10.1007/s11425-021-2055-5
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发表时间：
2023-06
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影响因子：
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通讯作者：
Wenhua Qian;Junhao Shen-;Wei Shi;Wenming Wu;Wei Yuan
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文献类型：
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作者：
Wenhua Qian;Junhao Shen-;Wei Shi;Wenming Wu;Wei Yuan
设是迹值为半有限因子的格拉斯曼投影空间之间的满射Lp-等距。在刻画有限因子酉群的满射Lp-同构的基础上，证明了φ或I-φ可以推广为一个 *-同构或一个 *-反同构.特别地，φ由 *-（反）同构给出，除非和是有限的，并且。
Letbe a surjectiveLp-isometry between Grassmann spaces of projections with the trace valuecin semifinite factorsand. Based on the characterization of surjectiveLp-isometries of unitary groups in finite factors, we show thatφorI—φcan be extended to a *-isomorphism or a *-anti-isomorphism. In particular,φis given by a *-(anti-)isomorphism unlessandare finite and.