Warianty tytułu
Abstrakty
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.
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.
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
498
Liczba stron
53
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- Fylde College, University of Lancaster, Lancaster LA1 4YF, United Kingdom
autor
- School of Mathematics, University of Leeds Leeds LS2 9JT, UK
autor
- School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, Wellington 6140, New Zealand
autor
- 5 Brookhill Crescent, Leeds LS17 8QB, UK
Bibliografia
Języki publikacji
EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm498-0-1
Identyfikatory
DOI
10.4064/dm498-0-1
Kolekcja
DML-PL
