Entire vectors for unbounded normal operators and abstract Cauchy problems  

作　　者：LI YangrongDepartment of Mathematics, Southwest Normal University, Chongqing 630715, China 

出　　处：《Chinese Science Bulletin》1997年第15期1253-1256,共4页

摘　　要：LET A be a closed operator on a Banach space X, and C~∞ (A)=∩_n~∞=1,D(A^n). The C~∞ vec-tor x is an entire vector for A if sum from n=0 to ∞ (t^n)/(n!)||A^n x||【∞ (1)for all t】0. We will write ε(A) for the set of all entire vectors for A. It is well known that the set of entire vectors for a self-adjoint operator is dense. Inthis note, we generalize this result to the situation of (unbounded) normal operators. We

关 键 词：C-SEMIGROUPS ANALYTIC SEMIGROUPS normal OPERATORS entire vectors. 

分 类 号：O152.7[理学—数学]