Operator monotone function
In linear algebra, the operator monotone function is an important type of real-valued function, first described by Charles Löwner in 1934.[1] It is closely allied to the operator concave and operator concave functions, and is encountered in operator theory and in matrix theory, and led to the Löwner–Heinz inequality.[2][3]
References
- ^ Löwner, K.T. (1934). "Über monotone Matrixfunktionen". Mathematische Zeitschrift. 38: 177–216. doi:10.1007/BF01170633. S2CID 121439134.
- ^ "Löwner–Heinz inequality". Encyclopedia of Mathematics.
- ^ Chansangiam, Pattrawut (2013). "Operator Monotone Functions: Characterizations and Integral Representations". arXiv:1305.2471 [math.FA].
Further reading
- Schilling, R.; Song, R.; Vondraček, Z. (2010). Bernstein functions. Theory and Applications. Studies in Mathematics. Vol. 37. de Gruyter, Berlin. doi:10.1515/9783110215311. ISBN 9783110215311.
- Hansen, Frank (2013). "The fast track to Löwner's theorem". Linear Algebra and Its Applications. 438 (11): 4557–4571. arXiv:1112.0098. doi:10.1016/j.laa.2013.01.022. S2CID 119607318.
- Chansangiam, Pattrawut (2015). "A Survey on Operator Monotonicity, Operator Convexity, and Operator Means". International Journal of Analysis. 2015: 1–8. doi:10.1155/2015/649839.
See also
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