On hyper‐reflexivity of some operator spaces

Abstract

ABSTRACT. In the present note, we define operator spaces with n-hyper-reflexive property, and prove n-hyper-reflexivity of some operator spaces

Rank-one perturbation of Toeplitz operators and reflexivity

“…Let t ∈ τ c. Since On the other hand, due to [8] we know that the algebra of analytic Toeplitz operators is hyperreflexive. Moreover, the space of all Toeplitz operators T is 2-hyperreflexive and κ 2 (T ) ≤ 2 (see [10,15]). We will show that the subspace M lm is 2-hyperreflexive.…”

Perturbation of Toeplitz operators and reflexivity

“…Since the space T is not reflexive it cannot be hyperreflexive, but we know due to [7,11] that T is 2-hyperreflexive with κ 2 (T ) ≤ 2. Now we will prove that the finite rank perturbation preserves 2-hyperreflexivity of T .…”

Projections onto the spaces of Toeplitz operators

“…In Section 7 we give a hyperreflexivity result for generalized Toeplitz operators. The one variable case was considered in [8].…”