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On measure-preserving transformations and doubly stationary symmetric stable processes

A. Gross, A. Weron (1995)

Studia Mathematica

In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...

On minimality and lp-complemented subspaces of Orlicz function spaces.

Francisco L. Hernández, Baltasar Rodríguez Salinas (1989)

Revista Matemática de la Universidad Complutense de Madrid

Several properties of the class of minimal Orlicz function spaces LF are described. In particular, an explicitly defined class of non-trivial minimal functions is shown, which provides concrete examples of Orlicz spaces without complemented copies of F-spaces.

On Musielak-Orlicz spaces isometric to L2 or L∞.

Anna Kaminska (1997)

Collectanea Mathematica

It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.

On P -convex Musielak-Orlicz spaces

Paweł Kolwicz, Ryszard Płuciennik (1995)

Commentationes Mathematicae Universitatis Carolinae

In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is P -convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16].

On Property β of Rolewicz in Köthe-Bochner Function Spaces

Paweł Kolwicz (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

It is proved that the Köthe-Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe-Bochner sequence spaces.

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