Equivalence of multi-norms

Dales, H.G. and Daws, M. and Pham, H. L. and Ramsden, P. (2014) Equivalence of multi-norms. Dissertationes Mathematicae (Rozprawy Matematyczne), 498. ISSN 0012-3862

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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 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 of some constants that arise. Several results depend on the classical theory of (q, p)-summing operators.

Item Type:
Journal Article
Journal or Publication Title:
Dissertationes Mathematicae (Rozprawy Matematyczne)
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
67561
Deposited By:
Deposited On:
15 Nov 2013 11:30
Refereed?:
Yes
Published?:
Published
Last Modified:
11 Feb 2020 08:17