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Equivalence of multi-norms

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Equivalence of multi-norms. / Dales, H.G.; Daws, M.; Pham, H. L. et al.
In: Dissertationes Mathematicae (Rozprawy Matematyczne), Vol. 498, 01.2014, p. 1-53.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dales, HG, Daws, M, Pham, HL & Ramsden, P 2014, 'Equivalence of multi-norms', Dissertationes Mathematicae (Rozprawy Matematyczne), vol. 498, pp. 1-53. https://doi.org/10.4064/dm498-0-1

APA

Dales, H. G., Daws, M., Pham, H. L., & Ramsden, P. (2014). Equivalence of multi-norms. Dissertationes Mathematicae (Rozprawy Matematyczne), 498, 1-53. https://doi.org/10.4064/dm498-0-1

Vancouver

Dales HG, Daws M, Pham HL, Ramsden P. Equivalence of multi-norms. Dissertationes Mathematicae (Rozprawy Matematyczne). 2014 Jan;498:1-53. doi: 10.4064/dm498-0-1

Author

Dales, H.G. ; Daws, M. ; Pham, H. L. et al. / Equivalence of multi-norms. In: Dissertationes Mathematicae (Rozprawy Matematyczne). 2014 ; Vol. 498. pp. 1-53.

Bibtex

@article{742c8c23312c4e319aad64f0099dd076,
title = "Equivalence of multi-norms",
abstract = "The theory of multi-norms was developed by H. G. Dales and M. E. Polyakov in a memoir that was published in Dissertationes Mathematicae. In that memoir, the notion of {\textquoteleft}equivalence{\textquoteright} of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent.In particular, we study when (p, q)-multi-norms defined on spaces Lr (Ω) are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show that the standard [t]-multi-norm defined on Lr (Ω) is not equivalent to a (p, q)-multi-norm in most cases, leaving some cases open. We discuss the equivalence of the Hilbert space multi-norm, the (p, q)-multi-norm, and the maximum multi-norm based on a Hilbert space. We calculate the value ofsome constants that arise.Several results depend on the classical theory of (q, p)-summing operators.",
author = "H.G. Dales and M. Daws and Pham, {H. L.} and P. Ramsden",
year = "2014",
month = jan,
doi = "10.4064/dm498-0-1",
language = "English",
volume = "498",
pages = "1--53",
journal = "Dissertationes Mathematicae (Rozprawy Matematyczne)",
issn = "0012-3862",
publisher = "Institute of Mathematics, Polish Academy of Sciences",

}

RIS

TY - JOUR

T1 - Equivalence of multi-norms

AU - Dales, H.G.

AU - Daws, M.

AU - Pham, H. L.

AU - Ramsden, P.

PY - 2014/1

Y1 - 2014/1

N2 - The theory of multi-norms was developed by H. G. Dales and M. E. Polyakov in a memoir that was published in Dissertationes Mathematicae. In that memoir, the notion of ‘equivalence’ of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent.In particular, we study when (p, q)-multi-norms defined on spaces Lr (Ω) are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show that the standard [t]-multi-norm defined on Lr (Ω) is not equivalent to a (p, q)-multi-norm in most cases, leaving some cases open. We discuss the equivalence of the Hilbert space multi-norm, the (p, q)-multi-norm, and the maximum multi-norm based on a Hilbert space. We calculate the value ofsome constants that arise.Several results depend on the classical theory of (q, p)-summing operators.

AB - The theory of multi-norms was developed by H. G. Dales and M. E. Polyakov in a memoir that was published in Dissertationes Mathematicae. In that memoir, the notion of ‘equivalence’ of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent.In particular, we study when (p, q)-multi-norms defined on spaces Lr (Ω) are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show that the standard [t]-multi-norm defined on Lr (Ω) is not equivalent to a (p, q)-multi-norm in most cases, leaving some cases open. We discuss the equivalence of the Hilbert space multi-norm, the (p, q)-multi-norm, and the maximum multi-norm based on a Hilbert space. We calculate the value ofsome constants that arise.Several results depend on the classical theory of (q, p)-summing operators.

U2 - 10.4064/dm498-0-1

DO - 10.4064/dm498-0-1

M3 - Journal article

VL - 498

SP - 1

EP - 53

JO - Dissertationes Mathematicae (Rozprawy Matematyczne)

JF - Dissertationes Mathematicae (Rozprawy Matematyczne)

SN - 0012-3862

ER -