Question
In an expository article clarifying this theorem to non-specialists, Paul Halmos asks “What does [this theorem] say?” An especially canonical form of this theorem yields an equivalence to a multiplication operator on a space given by a direct integral. The unitary case of this theorem may be quickly generalized by applying the Cayley transform and invoking a “multiplication theorem.” In functional analysis, this result is usually proven in a sequence of generalizations starting from compact operators and moving towards the unbounded (*) Hermitian case. When stated for self-adjoint operators, this result decomposes an operator as an integral with respect to a projection-valued measure. By this theorem, an operator T induces a resolution of the identity on a set denoted “sigma of T.” For 10 points, identify this theorem in linear algebra named for the set of a matrix’s eigenvalues. ■END■
Buzzes
Summary
Tournament | Edition | Exact Match? | TUH | Conv. % | Power % | Neg % | Average Buzz |
---|---|---|---|---|---|---|---|
2024 Chicago Open | 07/28/2024 | Y | 15 | 100% | 0% | 20% | 121.20 |