OAI/Analysis/IrrationalRotation/Spectral/WeightedShiftPolar.lean

GitHub source file

15 declarations, 0 contain sorry, 0 declared as axioms

  1. theorem OAI.Invariant233.WeightedShift.PolarSupport.diagonal_operator_injective line 24
  2. theorem OAI.Invariant233.WeightedShift.PolarSupport.operator_injective line 31
  3. theorem OAI.Invariant233.WeightedShift.PolarSupport.star_diagonal_polar line 35
  4. theorem OAI.Invariant233.WeightedShift.PolarSupport.diagonal_mul_polar line 47
  5. def OAI.Invariant233.WeightedShift.PolarSupport.sqrtRealWeight line 52
  6. theorem OAI.Invariant233.WeightedShift.PolarSupport.star_sqrtRealWeight_mul line 60
  7. theorem OAI.Invariant233.WeightedShift.PolarSupport.diagonal_nonneg line 68
  8. theorem OAI.Invariant233.WeightedShift.PolarSupport.star_shift_mul_shift line 73
  9. theorem OAI.Invariant233.WeightedShift.PolarSupport.shift_mul_star_shift line 80
  10. theorem OAI.Invariant233.WeightedShift.PolarSupport.shift_mem_unitary line 87
  11. theorem OAI.Invariant233.WeightedShift.PolarSupport.abs_operator_eq_abs_diagonal line 91
  12. theorem OAI.Invariant233.WeightedShift.PolarSupport.abs_operator line 107
  13. theorem OAI.Invariant233.WeightedShift.PolarSupport.operator_eq_shift_mul_abs line 111
  14. theorem OAI.Invariant233.WeightedShift.PolarSupport.ker_abs_operator_eq_bot line 116
  15. theorem OAI.Invariant233.WeightedShift.PolarSupport.positive_weight_polar_data line 121