Operator monotone function

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

1. Löwner, K.T. (1934). "Über monotone Matrixfunktionen". Mathematische Zeitschrift. 38. pp. 177–216.
2. "Löwner–Heinz inequality". Encyclopedia of Mathematics.
3. 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. 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.
• 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

• Matrix function
• Trace inequality