Operator-valued versions of matrix-norm inequalities

Jameson, Graham (2019) Operator-valued versions of matrix-norm inequalities. American Mathematical Monthly, 126 (9). pp. 809-815. ISSN 0002-9890

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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.

Item Type:
Journal Article
Journal or Publication Title:
American Mathematical Monthly
Additional Information:
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
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Deposited On:
23 Sep 2019 15:25
Last Modified:
31 Dec 2023 01:07