Equivalence of multi-norms

H. G. Dales, et al. Equivalence of multi-norms. 2014. <http://eudml.org/doc/286048>.

@book{H2014,
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 ’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 $L^\{r\}(Ω)$ 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 $L^\{r\}(Ω)$ 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 of some constants that arise. Several results depend on the classical theory of (q,p)-summing operators.},
author = {H. G. Dales, M. Daws, H. L. Pham, P. Ramsden},
keywords = {weak -summing norm; ; p); multi-norm; tensor product; ; q); standard -multi-norm; Hilbert multi-norm},
language = {eng},
title = {Equivalence of multi-norms},
url = {http://eudml.org/doc/286048},
year = {2014},
}

TY - BOOK
AU - H. G. Dales
AU - M. Daws
AU - H. L. Pham
AU - P. Ramsden
TI - Equivalence of multi-norms
PY - 2014
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 $L^{r}(Ω)$ 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 $L^{r}(Ω)$ 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 of some constants that arise. Several results depend on the classical theory of (q,p)-summing operators.
LA - eng
KW - weak -summing norm; ; p); multi-norm; tensor product; ; q); standard -multi-norm; Hilbert multi-norm
UR - http://eudml.org/doc/286048
ER -