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Asymptotically isometric and isometric copies of ℓ1 in some Banach function lattices

Kamińska A., Mastyło M.

Commentationes Mathematicae

2013

Vol. 53, No. 2

283--300

We identify the class of Calderón-Lozanovskii spaces that do not contain an asymptotically isometric copy of ℓ1, and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of ℓ1(n) for each integer n≥2. As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of ℓ1. In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of ℓ1(n) and ℓ1. The results are applied to obtain the description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.

Marcinkiewicz interpolation theorem and Marcinkiewicz Spaces

Maligranda L.

Wiadomości Matematyczne

2012

T. 48, Nr 2

157--171

Complex convexity of Orlicz-Lorentz spaces and its applications

Choi C., Kamińska A., Lee H. J.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 1

19-38

We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz-Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from d* (w, 1) into d(w, 1), where d*(w, 1) is a predual of a complex Lorentz sequence space d[w, 1), if and only if w [is an element of] c0 \ L2.

M-ideal properties in Marcinkiewicz spaces

Kamińska A., Lee H. J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

123-144

We study M-ideal properties of function and sequence Marcinkiewicz spaces. In particular we calculate the duals of the space L - L1 + L°° equipped with two standard norms and investigate when its subspace of order continuous elements is an M-ideal in E.