Edward Bormashenko, Nir Shvalb
Ramsey theory is applied to the analysis of operators acting on the functions belonging to the L2 Hilbert space. The operators form the vertices of the bi-colored graph. If the operators commute, they are joined by a yellow edge; if the operators do not commute, they are joined with a blue edge. Thus, a complete, non-directed, bi-colored graph arises, and Ramsey theory becomes applicable. If the graph contains six vertices/operators, at least one monochromatic (yellow or blue) triangle will necessarily be found in the graph. Therefore, the triad of operators forming the yellow triangle possesses a common set of eigenfunctions. The extension of the introduced approach to infinite sets of operators is addressed. Applications of the introduced approach to problems of classical and quantum mechanics are suggested.
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title={Operators in the Hilbert Space: the Ramsey Approach},
author={Edward Bormashenko and Nir Shvalb},
year={2024},
language={en}
}TY - JOUR TI - Operators in the Hilbert Space: the Ramsey Approach AU - Edward Bormashenko AU - Nir Shvalb PY - 2024 LA - en ER -
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