| Title:
|
Calculations in new sequence spaces (English) |
| Author:
|
de Malafosse, Bruno |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
1-18 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index $p>0$ of $r$-th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences. (English) |
| Keyword:
|
infinite linear system |
| Keyword:
|
operator of first order difference |
| Keyword:
|
Banach algebra with identity |
| Keyword:
|
BK space |
| MSC:
|
40H05 |
| MSC:
|
46A45 |
| idZBL:
|
Zbl 1164.40013 |
| idMR:
|
MR2310120 |
| . |
| Date available:
|
2008-06-06T22:50:18Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108045 |
| . |
| Reference:
|
[1] Maddox I. J.: Infinite matrices of operators.Springer-Verlag, Berlin, Heidelberg and New York, 1980. Zbl 0424.40002, MR 0568707 |
| Reference:
|
[2] de Malafosse B.: Properties of some sets of sequences and application to the spaces of bounded difference sequences of order $\mu $.Hokkaido Math. J. 31 (2002), 283–299. Zbl 1016.40002, MR 1914961 |
| Reference:
|
[3] de Malafosse B.: Sets of sequences that are strongly $\tau $-bounded and matrix transformations between these sets.Demonstratio Math. 36 1 (2003), 155–171. Zbl 1037.46008, MR 1968499 |
| Reference:
|
[4] de Malafosse B.: Variation of an element in the operator of first difference.Novi Sad J. Math. 32 1, (2002), 141–158. MR 1947951 |
| Reference:
|
[5] de Malafosse B.: On the set of sequences that are strongly $\alpha $-bounded and $\alpha $-convergent to naught with index $p$.Seminar. Mat. Torino 61 (2003), 13–32. MR 2034596 |
| Reference:
|
[6] de Malafosse B.: On matrix transformations and sequence spaces.Rend. Circ. Mat. Palermo (2) 52 (2003), 189–210. Zbl 1194.46005, MR 2002026 |
| Reference:
|
[7] de Malafosse B.: On some BK space.Internat. J. Math. Math. Sci. 28 (2003), 1783–1801. MR 1986671 |
| Reference:
|
[8] de Malafosse B.: Calculations on some sequence spaces.Internat. J. Math. Math. Sci. 29–32 (2004), 1653–1670. Zbl 1082.46007, MR 2085086 |
| Reference:
|
[9] de Malafosse B., Malkowsky E.: Sequence spaces and inverse of an infinite matrix.Rend. Circ. Mat. Palermo (2) 51 (2002), 277–294. Zbl 1194.46006, MR 1916930 |
| Reference:
|
[10] de Malafosse B., Malkowsky E.: Matrix transformations in the sets $\chi \left( \overline{N}_{p}\overline{N}_{q}\right) $ where $\chi $ is in the form s$_{\xi }$, or s$_{\xi }^{{{}^{\circ }}}$, or s$_{\xi }^{\left( c\right) }$.Filomat 17 (2003), 85–106. |
| Reference:
|
[11] Malkowsky E.: Linear operators in certain BK spaces.Bolyai Soc. Math. Stud. 5 (1996), 259–273. Zbl 0861.40007, MR 1432674 |
| Reference:
|
[12] Malkowsky E.: Linear operators between some matrix domains.Rend. Circ. Mat. Palermo (2) 68 (2002), 641–655. Zbl 1028.46015, MR 1975475 |
| Reference:
|
[13] Malkowsky E., Parashar S. D.: Matrix transformations in spaces of bounded and convergent difference sequences of order $m$.Analysis 17 (1997), 87–97. Zbl 0872.40002, MR 1451207 |
| Reference:
|
[14] Malkowsky E., Rakočević V.: An introduction into the theory of sequence spaces and measure of noncompactness.Zb. Rad. (Beogr.) 9 (17) (2000), 143–243. MR 1780493 |
| Reference:
|
[15] Wilansky A.: Summability through Functional Analysis.North-Holland Math. Stud. 85, 1984. Zbl 0531.40008, MR 0738632 |
| . |
