Hyperinvariant subspaces for sets of polynomially compact operators
Tóm tắt
We prove the existence of a non-trivial hyperinvariant subspace for several sets of polynomially compact operators. The main results of the paper are: (i) a non-trivial norm closed algebra
$$\mathcal {A}\subseteq \mathcal {B}(\mathscr {X})$$
which consists of polynomially compact quasinilpotent operators has a non-trivial hyperinvariant subspace; (ii) if there exists a non-zero compact operator in the norm closure of the algebra generated by an operator band
$$\mathcal {S}$$
, then
$$\mathcal {S}$$
has a non-trivial hyperinvariant subspace.
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