Vol. 8(2) July 2020, No. 21, pp. 231-243.

AN INFINITE-DIMENSIONAL SUBSPACE OF A NON-NORMABLE AND SEPARABLE FRECHET SPACE
Vol. 8(2) July 2020, No. 21, pp. 231-243
M. ALOYCE, S. KUMAR AND M. MPIMBO

 

Abstract

In this paper, we proved that if F is a non-normable and separable Fr´echet space, then there exists an infinite-dimensional subspace A ⊂ L(F) such that any non-zero operator T ∈ A is hypercyclic. We considered the existing partial solutions due to Bernal-Gonz´alez [15] and B`es and Conejero [9] to develop our results. An illustrative example is also provided


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