Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi mathvariant="double-struck">Z</mml:mi></mml:math>

Jiménez-Vargas, A.; Sepulcre, Juan Matías

doi:10.1016/j.jmaa.2012.10.024

Journal of Mathematical Analysis and Applications

2013

DOI: 10.1016/j.jmaa.2012.10.024

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Weighted composition operators on the predual and dual Banach spaces of Beurling algebras onZ

A. Jiménez-Vargas

Juan Matías Sepulcre

Abstract: Let v be a weight sequence on Z and let ψ, ϕ be complex-valued functions on Z such that ϕ (Z) ⊂ Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators C ψ,ϕ on predual Banach spaces c 0 (Z, 1/v) and dual Banach spaces ∞ (Z, 1/v) of Beurling algebras 1 (Z, v).

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Cited by 2 publications

References 17 publications

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Measurement and interpretation of spatially registered bar-forces in LC refining

Aigner

Olson

Wild

2020

Nordic Pulp &Amp; Paper Research Journal

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A high resolution rotary encoder and a piezo electric force sensor are implemented in a 16-inch laboratory-scale low consistency refiner to explore the effect of plate gaps on bar-force profiles. The sensor replaces a short length of a stator bar and measures normal and shear forces applied during the passage of each rotor bar. The rotary encoder data is used to locate the rotor bars relative to the stator bar in which the sensor is located. Previous work with this type of force sensor focuses primarily on the distribution of the maximum force measured during the passage of each rotor bar over the sensor or bar passing event, BPE. In this work, force profiles for bar passing events are registered to the position of rotor bars relative to the stator bar in which the sensor is located. These registered force profiles are measured for a range of plate gaps and two different pulp furnishes. The angular reference provided by the encoder makes it possible to generate mean force profiles. As force data for individual BPEs is highly variable, these mean force profiles have potential to shed light on the fundamental mechanisms of mechanical refining. For large gaps, there is a late peak in the force profiles that occurs toward the end of the bar passing event. For gaps that are less than the critical gap, below which fiber cutting occurs, there is an early peak in the force profiles that occurs at the start of the bar passing event. It is hypothesized that the early peak represents the corner force and, therefore, that corner force is causal in the onset of fiber cutting. To explore this hypothesis, a model is presented connecting corner force and friction force to the progression geometric variables during the bar passing event such as the bar edge length engaged at any point in the bar passing event and the area covered by the rotor bar on the force sensor at any point in the bar passing event.

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Measurement and interpretation of spatially registered bar-forces in LC refining

Aigner

Olson

Wild

2020

Nordic Pulp &Amp; Paper Research Journal

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Interpretation of force profiles in mill-scale LC refining

Aigner¹,

Olson²,

Sun³

et al. 2021

Nordic Pulp &Amp; Paper Research Journal

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A set of piezo electric force sensors is implemented in a 52-inch mill-scale low consistency refiner to explore the effect of varying operating conditions on bar force profiles. The sensor replaces a short length of a stator bar and measures normal and shear forces applied during the passage of each rotor bar. In previous work with this type of force sensor a rotary encoder was used to investigate force profiles for individual bar passing events (BPE) on a 16-inch laboratory-scale refiner. In the work presented here, force profiles for individual BPEs are identified based on key features in the time domain force data. The individual bar force profiles are classified as single peak events which feature one peak corresponding to the fiber compression force and as dual peak events corresponding to fiber compression force and the corner force. The bar passing events are then analysed based on their mean force profiles and their dual peak ratio in the bar passing event. Findings are compared and validated by previous work on bar force profiles. It is shown that dual peak events which are considered to represent the corner force, are present through out the whole range of refining and increase with increased refining energy. This increases the understanding of the way corner force contributes to the refining process. Furthermore, it is found that different radial positions on the stator plate are subjected to different force profiles. This is thought to be due to the difference in tangential speed and a change in the fiber and floc material properties at different radial positions.

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Weighted composition operators on the predual and dual Banach spaces of Beurling algebras onZ

Cited by 2 publications

References 17 publications

Measurement and interpretation of spatially registered bar-forces in LC refining

Measurement and interpretation of spatially registered bar-forces in LC refining

Interpretation of force profiles in mill-scale LC refining

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