A trace inequality for operators
β Scribed by Dinesh Singh
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 83 KB
- Volume
- 150
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this note, the matrix trace inequality for positive semidefinite matrices A and B, tr AB m β€ tr A 2m tr B 2m 1/2 is established, where m is an integer. The above inequality improves the result given by Yang (
Let A andB be positive operators and p, ct, s >/0. Assume either (1) A /> B and fl >~ max{-Β½(p + 2a), -Β½(i + 2a)}, or (2) A and B are invertible with log A ~> log B and /3 >/ -a. Then, for any continuous increasing function f on β’+ with f(0) = 0, the trace inequality Trf(A~(A'~BPA~)SA ~) <~ Trf(A (p
We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schro dinger operators. For example, let V be a continuous function on [0, 1] & /R & . For A/[1, ..., &], let &2 A be the Laplace operator on [0, 1] & with mixed Dirichlet Neumann boundary conditions .(x)=