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
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Operator-valued versions of matrix-norm inequalities
AU - Jameson, Graham
N1 - 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
PY - 2019/10/31
Y1 - 2019/10/31
N2 - 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.
AB - 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.
KW - MSC: Primary 47A63
KW - Secondary 15A45
KW - 15A60
U2 - 10.1080/00029890.2019.1639467
DO - 10.1080/00029890.2019.1639467
M3 - Journal article
VL - 126
SP - 809
EP - 815
JO - American Mathematical Monthly
JF - American Mathematical Monthly
SN - 0002-9890
IS - 9
ER -