Perturbation of Toeplitz operators and reflexivity
It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.
Reflexivity of bilattices
We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice we may associate a bilattice . Similarly, having a bilattice we may construct a subspace lattice . 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.
Hyperreflexivity of bilattices
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 we can construct the bilattice . Similarly, having a bilattice we may consider the lattice . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive...
Quasinormal operators are 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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