OAI/Analysis/KadisonKastler/VectorStateWitness.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

A unit-vector witness for a strict state inequality

A self-adjoint operator cannot have a state value above all its vector values. The proof uses only the quadratic-form order and positivity of states.

  1. theorem OAI.KadisonKastler.state_value_le_of_vector_bound line 20
  2. theorem OAI.KadisonKastler.exists_vector_state_gt line 53