Orbits and Capacity.

Authors :: Gohberg, I.
Alpay, D.
Arazy, J.
Atzmon, A.
Ball, J. A.
Ben-Artzi, A.
Bercovici, H.
Böttcher, A.
Clancey, K.
Coburn, L. A.
Curto, R. E.
Davidson, K. R.
Douglas, R. G.
Dijksma, A.
Dym, H.
Fuhrmann, P. A.
Gramsch, B.
Helton, J. A.
Kaashoek, M. A.
Kaper, H. G.
Source :: Spectral Theory of Linear Operators; 2007, p311-391, 81p
Publication Year :: 2007
Abstract: Let T be an operator on a Banach space X. By an orbit of T we mean a sequence (Tnx)n∞=0, where x ∈ X is a fixed vector. This notion, which originated in the theory of dynamical systems, is closely related to the concepts of local spectral radius and capacity of an operator. Further motivations come from stability problems of semigroups of operators and the invariant subspace problem. [ABSTRACT FROM AUTHOR]