| Title:
|
Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded (English) |
| Author:
|
Malkowsky, E. |
| Author:
|
Rakočević, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
505-522 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
BK spaces |
| Keyword:
|
bases |
| Keyword:
|
matrix transformations |
| Keyword:
|
measure of noncompactness |
| MSC:
|
40H05 |
| MSC:
|
46A45 |
| MSC:
|
47B07 |
| MSC:
|
47B37 |
| idZBL:
|
Zbl 1079.46504 |
| idMR:
|
MR1851544 |
| . |
| Date available:
|
2009-09-24T10:44:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127666 |
| . |
| Reference:
|
[1] R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii: Measures of noncompactness and condensing operators.Oper. Theory Adv. Appl. 55 (1992), Birkhäuser Verlag, Basel. MR 1153247, 10.1007/978-3-0348-5727-7_1 |
| Reference:
|
[2] A. M. Aljarrah and E. Malkowsky: BK spaces, bases and linear operators.Suppl. Rend. Circ. Mat. Palermo (2) 52 (1998), 177–191. MR 1644548 |
| Reference:
|
[3] J. Banás and K. Goebl: Measures of noncompactness in Banach spaces.Lecture Notes in Pure and Appl. Math. 60 (1980), Marcel Dekker, New York and Basel. MR 0566245 |
| Reference:
|
[4] G. H. Hardy: Divergent Series.Oxford University Press, 1973. MR 0030620 |
| Reference:
|
[5] E. Malkowsky: Linear operators in certain BK spaces.Bolyai Soc. Math. Stud. 5 (1996), 259–273. Zbl 0861.40007, MR 1432674 |
| Reference:
|
[6] E. Malkowsky and S. D. Parashar: Matrix transformations in spaces of bounded and convergent difference sequences of order $m$.Analysis 17 (1997), 87–97. MR 1451207, 10.1524/anly.1997.17.1.87 |
| Reference:
|
[7] E. Malkowsky and V. Rakočević: The measure of noncompactness of linear operators between certain sequence spaces.Acta Sci. Math. (Szeged) 64 (1998), 151–170. MR 1631981 |
| Reference:
|
[8] E. Malkowsky and V. Rakočević: The measure of noncompactness of linear operators between spaces of $m^{th}$-order difference sequences.Studia Sci. Math. Hungar. 35 (1999), 381–395. MR 1762251 |
| Reference:
|
[9] V. Rakočević: Funkcionalna analiza. Naučna knjiga.Beograd, 1994. |
| Reference:
|
[10] A. Wilansky: Summability through functional analysis.North-Holland Math. Stud. 85 (1984). Zbl 0531.40008, MR 0738632 |
| . |
