Operators Between Matrix Domains

Bruno de Malafosse (), Eberhard Malkowsky and Vladimir Rakočević
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Bruno de Malafosse: University of Le Havre (LMAH)
Eberhard Malkowsky: Univerzitet Union Nikola Tesla, Faculty of Management
Vladimir Rakočević: University of Niš, Department of Mathematics

Chapter Chapter 3 in Operators Between Sequence Spaces and Applications, 2021, pp 105-158 from Springer

Abstract: Abstract In this chapter, we apply the results of the previous chapters to characterize matrix transformations on the spaces of generalized weighted means and on matrix domains of triangles in BK spaces. We also establish estimates or identities for the Hausdorff measure of noncompactness of matrix transformations from arbitrary BK spaces with AK into c, $$c_{0}$$ c 0 and $$\ell _{1}$$ ℓ 1 , and also from the matrix domains of an arbitrary triangle in $$\ell _{p}$$ ℓ p , c and $$c_{0}$$ c 0 into c, $$c_{0}$$ c 0 and $$\ell _{1}$$ ℓ 1 . Furthermore we determine the classes of compact operators between the spaces just mentioned. Finally we establish the representations of the general bounded linear operators from c into itself and from the space $$bv^{+}$$ b v + of sequences of bounded variation into c, and the determination of the classes of compact operators between them.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-15-9742-8_3

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DOI: 10.1007/978-981-15-9742-8_3

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