### Perturbation of Toeplitz operators and reflexivity

It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.

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It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.

We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice $\mathcal{L}$ we may associate a bilattice ${\Sigma}_{\mathcal{L}}$. Similarly, having a bilattice $\Sigma $ we may construct a subspace lattice ${\mathcal{L}}_{\Sigma}$. Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.

The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice $\mathcal{L}$ we can construct the bilattice ${\Sigma}_{\mathcal{L}}$. Similarly, having a bilattice $\Sigma $ we may consider the lattice ${\mathcal{L}}_{\Sigma}$. In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive...

We will prove the statement in the title. We also give a better estimate for the hyperreflexivity constant for an analytic Toeplitz operator.

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