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Representations of Orlicz lattices

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Wnuk W.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction................................................................................................................................5 Preliminaries..............................................................................................................................5 A. Vector lattices......................................................................................................................6 B. Measure theory.................................................................................................................12 Musielak-Orlicz spaces............................................................................................................15 1. Some properties of Musielak-Orlicz spaces.......................................................................15 2. Isomorphisms between Musielak-Orlicz spaces.................................................................20 3. Drewnowski-Orlicz theorem...............................................................................................23 Representations of Orlicz lattices............................................................................................24 4. Basic properties of orthogonal additive modulars and examples of Orlicz lattices.............24 5. The Main Representation Theorem for Orlicz lattices........................................................32 6. Representation of Orlicz lattices by Orlicz spaces.............................................................40 7. Ultraproducts of some Orlicz lattices..................................................................................48 Notes and comments...............................................................................................................57 References..............................................................................................................................61

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Copies of $\mathbb R^{\mathbb N}$ in F-lattices

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Wnuk W.

Commentationes Mathematicae

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2016

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tom 56

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nr 2

EN

Modifying ideas presented in [14] we prove that a complete metrizable locally solid Riesz space $E$ contains a linear subspace linearly homeomorphic to $\mathbb R^{\mathbb N}$ iff $E$ contains a sublattice order isomorphic to $\mathbb R^{\mathbb N}$.

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Władysław Orlicz (1903-1990). A biography

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Maligranda L., Wnuk W.

Banach Center Publications

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2004

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tom 64

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nr 1

13-19

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Some Algebra Ideals Of Regular Operators

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Bayram E. B., Wnuk W.

Commentationes Mathematicae

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2013

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tom 53

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nr 2

EN

We investigate relationships joining the order continuity of a norm in a Banach lattice and some composition properties of L-weakly and M-weakly compact operators. Our results improve Proposition 3.6.16 from [5].

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Landau-type theorem for variable Lebesgue spaces

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Maligranda L., Wnuk W.

Commentationes Mathematicae

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2015

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tom 55

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nr 2

EN

We describe, using elementary methods, the K\"othe dual of variable Lebesgue spaces $L^{p(\cdot)},$ called also Nakano spaces, independenly for $p(\cdot) \in (1, \infty)$ and $p(\cdot) \in (0, 1)$. The case when $p(\cdot) \in [1, \infty]$ is also included.

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On the order-topological properties of the quotient space $L/L_{A}$

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Wnuk W.

Studia Mathematica

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1984

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tom 79

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nr 2

139-149

Ograniczanie wyników

3 Commentationes Mathematicae

1 Banach Center Publications

1 Studia Mathematica

6 Wnuk W.

2 Maligranda L.

1 Bayram E. B.

1 2016

1 2015

1 2013

1 2004

2 1984

Representations of Orlicz lattices

Copies of \(\mathbb R^{\mathbb N}\) in F-lattices

Władysław Orlicz (1903-1990). A biography

Some Algebra Ideals Of Regular Operators

Landau-type theorem for variable Lebesgue spaces

On the order-topological properties of the quotient space $L/L_{A}$