左乘算子的约化最小模

The reduced minimum modulus of left multiplicative operators

Banach空间X上的全体有界线性算子表示为B(X)对算子A∈B(X),左乘算子LA定义为LA(X)=AX,X∈B(X)。本文讨论了左乘算子LA的约化最小模与算子A的约化最小模的关系,得到γ(LA)≤γ(A)。特别地,对Hilbert空间上的算子A,证明了γ(LA)=γ(A)成立。

B（X） denotes the sets of all bounded linear operators defined on X. For A ∈ B（X）, the left multiplicative operator LA on B（X） is defined by LA （X） = AX, X∈（X）. Relationship between the reduced minimum modulus of the left multiplicative operator LA and of an operator A is discussed. γ（LA ）≤γ（A） is obtained. Particularly, for an operators A on a Hilbert space, γ（ LA ） = γ（ A ） .