Rank Nonincreasing Linear Maps on Vector Spaces

侯晋川; 张秀玲

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Rank Nonincreasing Linear Maps on Vector Spaces

更新时间：2026-09-14

- Rank Nonincreasing Linear Maps on Vector Spaces
- 矢量空间上的非增秩线性映射(英文)
- Issue 1, Pages: 1-9(2004)
- 作者机构：
  
  1. ,山西,太原,030051
  2. 山西师范大学数学与计算机学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2004
- 稿件说明：
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侯晋川, 张秀玲. Rank Nonincreasing Linear Maps on Vector Spaces[J]. 2004, (1): 1-9.
DOI：

侯晋川, 张秀玲. Rank Nonincreasing Linear Maps on Vector Spaces[J]. 2004, (1): 1-9. DOI：

摘要

　令V是域F上的向量空间

F(V)是作用于V上的所有有限秩线性变换构成的向量空间.给出F(V)上秩非增和完全非增秩线性映射的刻画.

Abstract

Let F(V) be the space of all finite rank linear transformations on a vector space V over a field F. Some characterizations of rank nonincreacing linear maps and completely rank nonincreasing linear maps on F(V) are presented.

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references

　GeL,HadwinD,HouJ,etal.RankNonincreasingLinearMapsonSpaceofBanachSpaceOperators[M].Preprint,2001.

　HerreroDA.ApproximationofHilbertSpaceOperators,Vol.I,ResearchNotesinMath.[M].PitmanAdvancedPublishingInc.,1982.

　HadwinD,LarsonD.Completelyrank-nonincreasinglinearmaps[J].J.Func.Anal.,2003,199:210-227.

　HouJ.Rank-preservinglinearmapsonB(X)[J].ScienceinChina(SeriesA),1989,23(8):929-940.

　LimMH.Linearmappingsonsecondsymmetricproductspacesthatpreservranklessthanorequaltoone[J].Lin.andMultilinearAlgebra,1990,26:187-193.

　LoewyR.Lineartransformationswhichpreserveordecreaserank[J].Lin.Alg.Appl.,1989,121:151-161.

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