Abstract
When A ∈ B ( H ) and B ∈ B ( K ) are given, we denote by M C the operator acting on the infinite dimensional separable Hilbert space H ⊕ K of the form M C = A C 0 B . In this paper, it is shown that if A is upper semi-Fredholm of finite ascent and infinite codimension, and if R ( B ) is closed of infinite kernel, then M C is upper semi-Fredholm of finite ascent for some C ∈ B ( K , H ) . In addition, we explore the hypercyclicity and supercyclicity for 2 × 2 upper triangular operator matrices on the Hilbert space.
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