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

What follows, and only in which direction

A separately typed modular bounded-witness module › What follows, and only in which direction · lines 1534–1546

Oai290-A@1#eq:localdefect

Put $C_{T} = P (T^{*} T)$ , and define

Λ_{s} (T) = δ ↓ 0 lim ∥ E_{D} ([s - δ, s + δ]) C_{T} E_{D} ([s - δ, s + δ]) ∥_{\infty} .

The limit exists by monotonicity; $C_{T}$ commutes with the spectral projections. Empty bands contribute zero.

Displayed formulas in this passage

Oai290-A@1#eq:localdefect · line 1537
$Λ_{s} (T) = δ ↓ 0 lim ∥ E_{D} ([s - δ, s + δ]) C_{T} E_{D} ([s - δ, s + δ]) ∥_{\infty} .$