Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences
Аутори
Malkowsky, EberhardRakočević, Vladimir
Veličković, Vesna
Остала ауторства
Milovanović, Gradimir V.Конференцијски прилог (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone
increasing sequence of positive real numbers, into the spaces wp0, wp and wp∞ of sequences
that are strongly summable to zero, strongly summable and strongly bounded by the Cesaro
method of order one and index p for 1 ≤ p < ∞. Furthermore, we prove estimates for the
Hausdorff measure of noncompactness of bounded linear operators from hd into wp, and
identities for the Hausdorff measure of noncompactness of bounded linear operators from
hd to wp0. We use these results to characterise the classes of compact operators from hd to
wp and wp0. Finally, we provide an example for some applications of our results and visualisations in crystallography.
Кључне речи:
The Hahn sequence space / spaces of strongly summable and sequences / bounded bounded linear operators / Hausdorff measure of noncompactness / compact operatorsИзвор:
Bulletin T.CLIII de l’Académie serbe des sciences et des arts, 2020, 25-41Издавач:
- Beograd : Académie Serbe des sciences et des arts
Напомена:
- Bulletin t. 153 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 45.
TY - CONF AU - Malkowsky, Eberhard AU - Rakočević, Vladimir AU - Veličković, Vesna PY - 2020 UR - https://dais.sanu.ac.rs/123456789/13422 AB - We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces wp0, wp and wp∞ of sequences that are strongly summable to zero, strongly summable and strongly bounded by the Cesaro method of order one and index p for 1 ≤ p < ∞. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from hd into wp, and identities for the Hausdorff measure of noncompactness of bounded linear operators from hd to wp0. We use these results to characterise the classes of compact operators from hd to wp and wp0. Finally, we provide an example for some applications of our results and visualisations in crystallography. PB - Beograd : Académie Serbe des sciences et des arts C3 - Bulletin T.CLIII de l’Académie serbe des sciences et des arts T1 - Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences SP - 25 EP - 41 UR - https://hdl.handle.net/21.15107/rcub_dais_13422 ER -
@conference{ author = "Malkowsky, Eberhard and Rakočević, Vladimir and Veličković, Vesna", year = "2020", abstract = "We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces wp0, wp and wp∞ of sequences that are strongly summable to zero, strongly summable and strongly bounded by the Cesaro method of order one and index p for 1 ≤ p < ∞. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from hd into wp, and identities for the Hausdorff measure of noncompactness of bounded linear operators from hd to wp0. We use these results to characterise the classes of compact operators from hd to wp and wp0. Finally, we provide an example for some applications of our results and visualisations in crystallography.", publisher = "Beograd : Académie Serbe des sciences et des arts", journal = "Bulletin T.CLIII de l’Académie serbe des sciences et des arts", title = "Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences", pages = "25-41", url = "https://hdl.handle.net/21.15107/rcub_dais_13422" }
Malkowsky, E., Rakočević, V.,& Veličković, V.. (2020). Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences. in Bulletin T.CLIII de l’Académie serbe des sciences et des arts Beograd : Académie Serbe des sciences et des arts., 25-41. https://hdl.handle.net/21.15107/rcub_dais_13422
Malkowsky E, Rakočević V, Veličković V. Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences. in Bulletin T.CLIII de l’Académie serbe des sciences et des arts. 2020;:25-41. https://hdl.handle.net/21.15107/rcub_dais_13422 .
Malkowsky, Eberhard, Rakočević, Vladimir, Veličković, Vesna, "Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences" in Bulletin T.CLIII de l’Académie serbe des sciences et des arts (2020):25-41, https://hdl.handle.net/21.15107/rcub_dais_13422 .