Manuscript Oai290-A@1 · Oai290-A.tex · corollary · 7c6e104a

Corollary: A named asymptotic defect contract

A separately typed modular bounded-witness module › What follows, and only in which direction · lines 1575–1591 · proof included or linked

Oai290-A@1#cor:intertwining

Suppose a fixed $T \in B (H)$ obeys the additional contract

∥ φ w_{n} - e^{s} w_{n} φ ∥_{M_{*}} \to 0, n sup ∥ w_{n} ∥ < \infty ⟹ ∥ T w_{n} ξ ∥ \to 0.

Then $Λ_{s} (T) = 0$ .

Proof. Lemma lem:modularlocal supplies the premise for every bounded shrinking-band sequence. Apply Corollary cor:boundeddefect.

Displayed formulas in this passage

unlabeled · line 1578
$∥ φ w_{n} - e^{s} w_{n} φ ∥_{M_{*}} \to 0, n sup ∥ w_{n} ∥ < \infty ⟹ ∥ T w_{n} ξ ∥ \to 0.$