黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2009年
2期
182-184,189
,共4页
上三角矩阵代数%k-幂等矩阵%映射
上三角矩陣代數%k-冪等矩陣%映射
상삼각구진대수%k-멱등구진%영사
upper triangular matrix algebras%k-potent matrix%map
设C是复数域,T2(C)是C上2×2上三角矩阵代数.Tk2(C)记T2(C)中的所有k-幂等矩阵构成的子集,这里k≥2.若映射φ满足:由A-λB∈Tk2(C)可以推出φ(A)-λφ(B)∈Tk2(C),则称φ是保k幂等的.用Ф(C)记所有从T2(C)到自身的上述单射φ的集合.给出Ф(C)中算子的形式.
設C是複數域,T2(C)是C上2×2上三角矩陣代數.Tk2(C)記T2(C)中的所有k-冪等矩陣構成的子集,這裏k≥2.若映射φ滿足:由A-λB∈Tk2(C)可以推齣φ(A)-λφ(B)∈Tk2(C),則稱φ是保k冪等的.用Ф(C)記所有從T2(C)到自身的上述單射φ的集閤.給齣Ф(C)中算子的形式.
설C시복수역,T2(C)시C상2×2상삼각구진대수.Tk2(C)기T2(C)중적소유k-멱등구진구성적자집,저리k≥2.약영사φ만족:유A-λB∈Tk2(C)가이추출φ(A)-λφ(B)∈Tk2(C),칙칭φ시보k멱등적.용Ф(C)기소유종T2(C)도자신적상술단사φ적집합.급출Ф(C)중산자적형식.
Let C be the field of complex numbers.Let T2(C) be the 2×2 upper triangular matrix algebras over C,and Tk2(C) be the subset of all k-potent matrices in T2(C),where k≥2.A map is said to preserve k-potence if A-λB∈Tk2(C) implies that φ(A)-λφ(B)∈Tk2(C)for all A,B∈T2(C) and
