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Matrix mappings and general bounded linear operators on the space $bv$

In: Mathematica Slovaca, vol. 68, no. 2
Ivana Djolović - Katarina Petković - Eberhard Malkowsky

Details:

Year, pages: 2018, 405 - 414
Keywords:
$BK$ spaces, sequences of bounded variation, matrix mappings, bounded and compact linear operators
About article:
If $X$ and $Y$ are $FK$ spaces, then every infinite matrix $A\in (X,Y)$ defines a bounded linear operator $LA\in B(X,Y)$ where $LA(x)=Ax$ for each $x\in X$. But the converse is not always true. Indeed, if $L$ is a general bounded linear operator from $X$ to $Y$, that is, $L\in B(X,Y)$, we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space $bv$ into the spaces $\ell$, $c$ and $c0$. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the difference between general bounded linear operators between some sequence spaces and the matrix operators associated with matrix transformations.
How to cite:
ISO 690:
Djolović, I., Petković, K., Malkowsky, E. 2018. Matrix mappings and general bounded linear operators on the space $bv$. In Mathematica Slovaca, vol. 68, no.2, pp. 405-414. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0111

APA:
Djolović, I., Petković, K., Malkowsky, E. (2018). Matrix mappings and general bounded linear operators on the space $bv$. Mathematica Slovaca, 68(2), 405-414. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0111
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