A remark on contraction semigroups on banach spaces
Abstract
Let X be a complex Banach space and let J:X→X#x002A; be a duality section on X (that is, 〈x, J(x)〉=∥J(x)∥∥x∥=∥J(x)∥2)=∥x∥2). For any unit vector x and any (C0) contraction semigroup T={etA: t≥0}, Goldstein proved that if X is a Hilbert space and ∣〈T(t)x, j(x)〉∣→1 as t→∞, then x is an eigenvector of A corresponding to a purel imaginary eigenvalue. In this article, we prove that a similar result holds if X is a strictly convex complex Banach space. © 1995 Oxford University Press.
Publication Title
Bulletin of the London Mathematical Society
Recommended Citation
Lin, P. (1995). A remark on contraction semigroups on banach spaces. Bulletin of the London Mathematical Society, 27 (2), 169-172. https://doi.org/10.1112/blms/27.2.169
COinS
