Meaning
The local linking defect measures how far a selected local correspondence is from having the required graph realization.
It minimizes the combined failures of w∗w=e_A, ww∗=e_B, and wAw∗=B in the specified norms and topology. The local correspondence is graph-like when the infimum is attained at zero. The topology and boundedness conventions are part of the test.
Example (illustrative)
A unitary w with wAw∗=B gives zero for all three terms. A sequence w_n making them arbitrarily small shows only that the infimum is zero until a valid limiting w has been obtained.
Scope and limits
Zero infimum is weaker than attained zero. Compactness or another attainment argument is needed before approximate graph behavior becomes an actual spatializer.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.9.