Source-pinned research
Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.
This index contains 12 research declarations. Search 10,000 more complete Mathlib declarations.
12 results
Clear filtersLinearPMap.IsClosable.add_continuous
Plain-language statement
Closability is preserved upon adding a continuous operator.
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsClosed.add_continuous
Plain-language statement
Closedness is preserved upon adding a continuous operator.
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsFormalAdjoint.unitaryConj
Plain-language statement
Unitary conjugation preserves formal adjointness. If A is a formal adjoint of B, then u A u⁻¹ is a formal adjoint of u B u⁻¹. Unitary conjugation preserves symmetry when A = B.
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsSymmetric.closure
Plain-language statement
The closure of a symmetric densely-defined operator is symmetric: T†† is a symmetric closed extension of T, so it extends T.closure, whose symmetry then descends.
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsSymmetric.isSelfAdjoint_of_range_eq_top
Plain-language statement
Self-adjointness from surjectivity of T ± i: a symmetric, densely-defined operator T for which T + I • 1 and T - I • 1 both have full range is self-adjoint.
Source project: Physlib
Person-level attribution pending.
LinearPMap.unitaryConj_sub_smul_surjective
Plain-language statement
If A - z is surjective for a scalar z : ℂ, then so is u A u⁻¹ - z.
Source project: Physlib
Person-level attribution pending.