Measure of noncompactness of linear operators between spaces of sequences that are ( N ¯ , q ) summable or bounded

Eberhard Malkowsky; V. Rakočević

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 3, page 505-522
  • ISSN: 0011-4642

Abstract

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In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are ( N ¯ , q ) summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y . Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.

How to cite

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Malkowsky, Eberhard, and Rakočević, V.. "Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded." Czechoslovak Mathematical Journal 51.3 (2001): 505-522. <http://eudml.org/doc/30652>.

@article{Malkowsky2001,
abstract = {In this paper we investigate linear operators between arbitrary BK spaces $X$ and spaces $Y$ of sequences that are $(\bar\{N\},q)$ summable or bounded. We give necessary and sufficient conditions for infinite matrices $A$ to map $X$ into $Y$. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.},
author = {Malkowsky, Eberhard, Rakočević, V.},
journal = {Czechoslovak Mathematical Journal},
keywords = {BK spaces; bases; matrix transformations; measure of noncompactness; BK spaces; bases; matrix transformations; measure of noncompactness},
language = {eng},
number = {3},
pages = {505-522},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Measure of noncompactness of linear operators between spaces of sequences that are $(\bar\{N\},q)$ summable or bounded},
url = {http://eudml.org/doc/30652},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Malkowsky, Eberhard
AU - Rakočević, V.
TI - Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 505
EP - 522
AB - In this paper we investigate linear operators between arbitrary BK spaces $X$ and spaces $Y$ of sequences that are $(\bar{N},q)$ summable or bounded. We give necessary and sufficient conditions for infinite matrices $A$ to map $X$ into $Y$. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.
LA - eng
KW - BK spaces; bases; matrix transformations; measure of noncompactness; BK spaces; bases; matrix transformations; measure of noncompactness
UR - http://eudml.org/doc/30652
ER -

References

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  9. Funkcionalna analiza. Naučna knjiga, Beograd, 1994. (1994) 
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