A note on the parallel sum

By using a variational principle we find a necessary and sufficient condition for an operator to majorise the parallel sum of two positive definite operators. This result is then used as a vehicle to create new operator inequalities involving the parallel sum.

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Bibliographic Details
Published in:Linear algebra and its applications 2022-03, Vol.636, p.69-76
Main Author: Hansen, Frank
Format: Article
Language:English
Subjects:
Linear algebra
Operator inequality
The parallel sum
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Description
Summary:By using a variational principle we find a necessary and sufficient condition for an operator to majorise the parallel sum of two positive definite operators. This result is then used as a vehicle to create new operator inequalities involving the parallel sum.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.11.013