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 se...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展开更多
文摘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
