More Operator Versions of the Schwarz Inequality
โ Scribed by Rajendra Bhatia; Chandler Davis
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 42 KB
- Volume
- 215
- Category
- Article
- ISSN
- 0010-3616
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๐ SIMILAR VOLUMES
Let A be an n ร n positive definite symmetric real matrix with n eigenvalues ฮป 1 , ฮป 2 , . . . , ฮป n and let x and y be two n ร 1 vectors with the angle ฯ. This paper proves the following inequality (x T Ax)(y T Ay).
We prove a version of the Schwarz Lemma in which the images of two points are ลฝ . known. Two classical results due to Dieudonne and Rogosinski are simple
Using the theory of connections developed in a paper by Kubo and Ando, operator versions of many classical inequalities are obtained. Finally, it is shown how abstract solidarities, an extension of the Kubo-Ando theory, can be used to obtain operator inequalities.