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    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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Operator-valued versions of matrix-norm inequalities

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Operator-valued versions of matrix-norm inequalities. / Jameson, Graham.
In: American Mathematical Monthly, Vol. 126, No. 9, 31.10.2019, p. 809-815.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Jameson, G 2019, 'Operator-valued versions of matrix-norm inequalities', American Mathematical Monthly, vol. 126, no. 9, pp. 809-815. https://doi.org/10.1080/00029890.2019.1639467

APA

Vancouver

Jameson G. Operator-valued versions of matrix-norm inequalities. American Mathematical Monthly. 2019 Oct 31;126(9):809-815. Epub 2019 Oct 23. doi: 10.1080/00029890.2019.1639467

Author

Jameson, Graham. / Operator-valued versions of matrix-norm inequalities. In: American Mathematical Monthly. 2019 ; Vol. 126, No. 9. pp. 809-815.

Bibtex

@article{38cea26266f24cde993d8cc1cd54b2fa,
title = "Operator-valued versions of matrix-norm inequalities",
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.",
keywords = "MSC: Primary 47A63, Secondary 15A45, 15A60",
author = "Graham Jameson",
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",
year = "2019",
month = oct,
day = "31",
doi = "10.1080/00029890.2019.1639467",
language = "English",
volume = "126",
pages = "809--815",
journal = "American Mathematical Monthly",
issn = "0002-9890",
publisher = "Mathematical Association of America",
number = "9",

}

RIS

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 -