Hilbert space operator
C36563
concept
A Hilbert space operator is a linear transformation defined on a (subspace of a) Hilbert space that maps vectors to vectors in a way compatible with the space’s inner product structure, often studied via its continuity, boundedness, and spectral properties.
All labels observed (7)
| Label | Occurrences |
|---|---|
| quantum mechanical operator | 3 |
| Fourier multiplier operator | 1 |
| Hamiltonian operator | 1 |
| Hilbert space operator canonical | 1 |
| projection operator | 1 |
| relativistic operator | 1 |
| self-adjoint operator | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: Hilbert space operator
Generated description
A Hilbert space operator is a linear transformation defined on a (subspace of a) Hilbert space that maps vectors to vectors in a way compatible with the space’s inner product structure, often studied via its continuity, boundedness, and spectral properties.
Instances (6)
| Instance | Via concept surface |
|---|---|
|
Hilbert–Schmidt operator
linked to:
Hilbert–Schmidt operators
|
— |
| Dirac Hamiltonian | quantum mechanical operator |
| four-momentum operator | quantum mechanical operator |
| Pauli–Lubanski pseudovector | quantum mechanical operator |
| Riesz transforms | Fourier multiplier operator |
| Riesz projection | projection operator |