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A Banach space is said to be if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex , then dim , where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic division ring....
Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.
In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.
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