definition · fr-2-definition-5-1
Directed graph defect
Definition in the source manuscript fusion-reconstruction
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Statement
For a densely defined total map on a countable increasing algebraic union, define . This equals .
Meaning and scope
The graph defect tests what survives when finite source vectors vanish in the total norm. It is zero exactly when the induced operator is closable.
Example
The averaging sequence for scalar summation has defect value ; scalar multiples yield every complex defect value.
The paper page includes the reader corrections accompanying this edition.
Source
Paper 2, Definition 5.1. Research note — not peer reviewed.
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