有MP逆的Abel范畴中态射方程αxα*=β的非负定解

Abstract

Abstract:

In this paper the authors discuss nonnegativedefinite solutionsto the morphism equation αxα*=β in Abel categories
with MP inverse. As their application, the authors give some relevant results of the matrix equatiom AXA*=B　over pdivision ring.

Key words: Abel categories, MP inverse, Nonnegativedefinite morphism, Positivedefinite morphism

CLC Number:

18E10

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DIAO Xiao-Mei, SUN Zhi-Min. Nonnegativedefinite Solutions to the MorphismEquation αxα*=β in Abel Categories with MP Inverse[J].Acta mathematica scientia,Series A, 2004, 4(5): 537-542.

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References

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［2］Frey P. Abelian Categories. New York: Harper & Row, 1964
［3］李桃生. 有满单分解态射的MoorePenrose逆. 数学学报，1993，36(1)：60-67
［4］李桃生. Abel范畴中的线性态射方程. 华中师范大学学报，1993，27：415-418
［5］李桃生. 范畴与同调代数基础. 武汉：华中师范大学出版社，1988
［6］李桃生. p除环上子空间的商与和. 数学物理学报，1995，15(4)：467-472

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Nonnegativedefinite Solutions to the MorphismEquation αxα*=β in Abel Categories with MP Inverse

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