Moduli and characteristics of monotonicity in some Banach lattices.
Some basic properties of generalized Calderon-Lozanovskiî.
Some remarks on level functions and their applications
A comparison of the level functions considered by Halperin and Sinnamon is discussed. Moreover, connections between Lorentz-type spaces, down spaces, Cesàro spaces, and Sawyer's duality formula are explained. Applying Sinnamon's ideas, we prove the duality theorem for Orlicz−Lorentz spaces which generalizes a recent result by Kamińska, Leśnik, and Raynaud (and Nakamura). Finally, some applications of the level functions to the geometry of Orlicz−Lorentz spaces are presented.
Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm
We first prove that the property of strict monotonicity of a Köthe space and/or of its Köthe dual can be used successfully to compare the supports of and , where . Next we prove that any element with is a point of order smoothness in , whenever is an order continuous Köthe space. Finally, we present formulas for the characteristic of monotonicity of Orlicz function spaces endowed with the Orlicz norm in the case when the generating Orlicz function does not satisfy suitable -condition...
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