Home > Research > Publications & Outputs > Operator-valued versions of matrix-norm inequal...

Electronic data

  • opineq.amm

    Rights statement: This is an Accepted Manuscript of an article published by Taylor & Francis in The American Mathematical Monthly on 23/10/2019 available online: https://maa.tandfonline.com/doi/full/10.1080/00029890.2019.1639467

    Accepted author manuscript, 151 KB, PDF document

    Embargo ends: 23/10/20

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

View graph of relations

Operator-valued versions of matrix-norm inequalities

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>31/10/2019
<mark>Journal</mark>American Mathematical Monthly
Issue number9
Volume126
Number of pages7
Pages (from-to)809-815
Publication statusPublished
Early online date23/10/19
Original languageEnglish

Abstract

We describe a rather striking extension of a wide class of inequalities. Some famous classical inequalities, such as those of Hardy and Hilbert, equate to the evaluation of the norm of a matrix operator. Such inequalities can be presented in two versions, linear and bilinear. We show that in all such inequalities, the scalars can be replaced by operators on a Hilbert space, with the conclusions taking the form of an operator inequality in the usual sense. With careful formulation, a similar extension applies to the Cauchy–Schwarz inequality.

Bibliographic note

This is an Accepted Manuscript of an article published by Taylor & Francis in The American Mathematical Monthly on 23/10/2019 available online: https://maa.tandfonline.com/doi/full/10.1080/00029890.2019.1639467