(Z)条件下正则cosine函数乘积扰动下的不变性质  

Stable Properties of Regularized Cosine Functions under Multiplicative Perturbations with the (Z)-condition

作　　者：李芳[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《中国科学技术大学学报》2001年第4期386-393,共8页JUSTC

基　　金：国家自然科学基金 (10 0 710 79)资助项目

摘　　要：设A生成Banach空间X上的指数有界C cosine函数C(t) .论文将讨论在满足(Z )条件的乘积扰动下 ,C(t)的范数连续性、局部Lipschitz连续性 ,局部紧性仍然保持不变 ,并得到一个逼近结果 .同时 ,也得到 (Z)Let A be the infinitesimal generator of an expo ne ntially bounded C cosine operator function C(t) in a Banach spa ce X. This paper mainly discusses the properties of C(t), such as the norm continuity, local Lipschitz continuity, local compactness, which are preserved under the multiplicative perturbation with the (Z *) condition. The main results of this paper are as follows. Assume that D(A) is dense in X and Z satisfies the (Z *) condition . (i) Suppose that B ∈L(Z, C(X)) and BC=CB. If C(t) is norm continuou s for t>0 (resp. locally Lipschitz continuous),then so is the exponentially bounded C cosine function generated by (I+B)A. If I+B is a left invertible operator, then the exponentially bounded C cosine function generated by A(I+B) is also norm continuous for t>0 (resp. loc ally Lipschitz continuous). (ii) Suppose that B ∈L(Z, C(X)) and BC=CB. If C(t) is compact and n orm continuous for t>0, then the exponentially bounded C cosine function generated by (I+B)A is locally compact and norm continuous for t >0. If I+B is left invertible, then so is the exponentially bounded [WTBX ]C cosine function generated by A(I+B). (iii) Suppose that B n ∈L(Z,C(X)) and B n C=CB n (n ∈N). Denote by C ln (·) and C rn (·) the exponentially bounded C [ WTBZ]cosine functions generated by (I+B n)A and A(I+B n), respectively . If B n→B 0 in the operator norm as n→∞, then C ln (t)→C l0 (t), where convergence is in the operator norm and takes place uniformly on compact intervals. The same is true for C rn (t)→C r0 (t), if I+B 0 is left invertible. In addition, similar results were obtained under the (Z) condition.

关 键 词：正则cosine函数 乘积扰动 (Z＊)条件 BANACH空间 范数连续性 局部Lipschitz连续性 

分 类 号：O177.2[理学—数学]