Abstract
We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.
| Original language | English |
|---|---|
| Pages (from-to) | 1283-1295 |
| Number of pages | 13 |
| Journal | International Journal of Mathematics |
| Volume | 21 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2010 Oct 1 |
Keywords
- Godunova's inequality
- Hardy's inequality
- Hardy-Hilbert's inequality
- Inequalities
- operator convex functions
- positive operator
- weights
ASJC Scopus subject areas
- Mathematics(all)
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Hansen, F., Krulić, K., Pečarić, J., & Persson, L. E. (2010). Generalized noncommutative Hardy and Hardy-Hilbert type inequalities. International Journal of Mathematics, 21(10), 1283-1295. https://doi.org/10.1142/S0129167X10006501