TY - JOUR
AU - Gillespie, T. A.
AB -  Bull. London Math. Soc. 45 (2013) 889­893 Modern approaches to the invariant-subspace problem (Cambridge Tracts in Mathematics 188) By Isabelle Chalendar and Jonathan R. Partington: 285 pp., £45.00 (US$75.00) isbn 978-1-107-01051-2 (Cambridge University Press, Cambridge, 2011). e 2013 London Mathematical Society doi:10.1112/blms/bdt016 Published online 4 April 2013 The invariant-subspace problem asks whether every bounded linear operator T on a complex Banach space X of dimension at least 2 has a non-trivial closed invariant subspace; that is, does there exist a closed subspace M of X , different from both {0} and X , such that T (M) M? If X is finite-dimensional, then T will have an eigenvector and hence a onedimensional invariant subspace whilst, if X is non-separable and 0 = x X , then the closed linear span of {T n x : n = 0, 1, 2, . . .} is non-trivial and T -invariant. Thus the interest in the problem lies in the case when X is infinite-dimensional and separable. The problem dates back at least as far as the 1950s when Aronszajn and Smith [1] gave a positive solution for compact operators on Banach spaces, the Hilbert space case of this result having 
TI - Book Review: Modern approaches to the invariant-subspace problem (Cambridge Tracts in Mathematics 188) By Isabelle Chalendar and Jonathan R. Partington
JF - Bulletin of the London Mathematical Society
DO - 10.1112/blms/bdt016
DA - 2013-08-01
UR - https://www.deepdyve.com/lp/oxford-university-press/book-review-modern-approaches-to-the-invariant-subspace-problem-rMBzXLZdBm
SP - 889
EP - 891
VL - 45
IS - 4
DP - DeepDyve
ER -