In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.
We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.
We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak space; symmetric sets of constant ratio occur in an unexpected way.
We obtain the necessary and sufficient condition of weak star uniformly rotund point in Orlicz spaces.
The concept of WM point is introduced and the criterion of WM property in Orlicz function spaces endowed with Luxemburg norm is given.
In this paper, we introduce the concept of WM point and obtain the criterion of WM points for Orlicz function spaces endowed with Orlicz norm and the criterion of WM property for Orlicz space.
We obtain the criterion of the WM property for Orlicz sequence spaces endowed with the Orlicz norm.
For Orlicz spaces endowed with the Orlicz norm and the Luxemburg norm, the criteria for uniformly nonsquare points and nonsquare points are given.
Let 1 ≤ p < 2 and let be the classical -space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable spans in a subspace isomorphic to some Orlicz sequence space . We give precise connections between M and f and establish conditions under which the distribution of a random variable whose independent copies span in is essentially unique.
It is shown that in the Dirichlet space , two invariant subspaces ℳ ₁, ℳ ₂ of the Dirichlet shift are unitarily equivalent only if ℳ ₁ = ℳ ₂.
We characterize unitary equivalence of quasi-free Hilbert modules, which complements Douglas and Misra's earlier work [New York J. Math. 11 (2005)]. We first confine our arguments to the classical setting of reproducing Hilbert spaces and then relate our result to equivalence of Hermitian vector bundles.