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 -