Sentence examples for continuous norms from inspiring English sources

This means that ({bar{r}_{n}}_{n=1}^{+infty}) does not have equi-absolutely continuous norms in (E^{Psi}_{h} (Omega)).

Mainly, we focus on the problem when the unit ball BH:="{f∈H:‖f‖p⩽1} of a Λ(p -space H has equi-absolutely continuous norms in Lp -space

Conversely, if a set (Asubset E^{varphi}(Omega)) is relatively compact, then all the functions in A have equi-absolutely continuous norms and A is relatively compact with respect to local convergence in measure.

We say that the operator (T: L^{Phi}(Omega) rightarrow L^{Psi}(Omega)) is equi-absolutely continuous if for any bounded set (A subset L^{Phi}(Omega)) all functions of the set (T (A)subset L^{Psi}(Omega)) have equi-absolutely continuous norms.

If the functions in a set (Asubset L^{varphi}(Omega)) all have equi-absolutely continuous norms and A is relatively compact with respect to local convergence in measure, then A is relatively compact in (E^{varphi}(Omega)), the subspace of absolutely continuous functions in (L^{varphi}(Omega)).

Suppose that X does not have an absolutely continuous norm.

If X has no absolute continuous norm, then (R X,a)=1+a ).

Since (Phinotinoverline{delta}_{2}), we see that (l_{Phi}) has no absolutely continuous norm.

A Köthe sequence space X is said to have an absolutely continuous norm if (X_{a}=X).

In what follows, E will always denote a minimal symmetric quasi-Banach space with order continuous norm.

Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm.