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On Musielak-Orlicz spaces isometric to L or L.

Anna Kaminska — 1997

Collectanea Mathematica

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

Order convexity and concavity of Lorentz spaces Λ p , w , 0 < p < ∞

Anna KamińskaLech Maligranda — 2004

Studia Mathematica

We study order convexity and concavity of quasi-Banach Lorentz spaces Λ p , w , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that Λ p , w contains an order isomorphic copy of l p . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for Λ p , w . We conclude with a characterization of the type and cotype of Λ p , w in the case when Λ p , w is a normable space.

Asymptotically isometric and isometric copies of 1 in some Banach function lattices

Anna KamińskaMieczysław ~Mastyło — 2013

Commentationes Mathematicae

We identify the class of Caldern-Lozanovskii spaces that do not contain an asymptotically isometric copy of 1 , 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 1 ( n ) for each integer n 2 . As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz...

Complex rotundities and midpoint local uniform rotundity in symmetric spaces of measurable operators

Małgorzata Marta CzerwińskaAnna Kamińska — 2010

Studia Mathematica

We investigate the relationships between strongly extreme, complex extreme, and complex locally uniformly rotund points of the unit ball of a symmetric function space or a symmetric sequence space E, and of the unit ball of the space E(ℳ,τ) of τ-measurable operators associated to a semifinite von Neumann algebra (ℳ,τ) or of the unit ball in the unitary matrix space C E . We prove that strongly extreme, complex extreme, and complex locally uniformly rotund points x of the unit ball of the symmetric...

Dual spaces to Orlicz-Lorentz spaces

Anna KamińskaKarol LeśnikYves Raynaud — 2014

Studia Mathematica

For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space Λ φ , w or the sequence space λ φ , w , equipped with either the Luxemburg or Amemiya norms. The first description is via the modular i n f φ ( f * / | g | ) | g | : g w , where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular I φ ( ( f * ) / w ) w ,where (f*)⁰ is Halperin’s level function...

Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals

Malgorzata M. CzerwińskaAnna H. Kaminska — 2017

Commentationes Mathematicae

This is a review article of geometric properties of noncommutative symmetric spaces of measurable operators E ( , τ ) , where is a semifinite von Neumann algebra with a faithful, normal, semifinite trace τ , and E is a symmetric function space. If E c 0 is a symmetric sequence space then the analogous properties in the unitary matrix ideals C E are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss...

Complex Convexity of Orlicz-Lorentz Spaces and its Applications

Changsun ChoiAnna KamińskaHan Ju Lee — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

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 wi ∈ c₀∖ℓ₂.

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