算子n次幂的零维与半正则性

The Nullity of the n-powers of an Operator and Semi-regularity

对线性算子T的n次幂Tn,讨论其零空间N(Tn)的维数α(Tn):=dim N(Tn)与n.α(T)的关系,证明了当T是上半-Fredholm算子时,α(Tn)=n.α(T)对一切自然数n成立当且仅当T是半正则的.

Discuss the relationship between the nullity of the n-powers of a linear operator T·α（T^n）：=dim N（T^n） and n·α（T）,prove that when T is a upper semi-Fredholm operator, α（T^n）=n·α（T） holds if and only if T is a semi-regular,for all natural number n.