| Title:
|
Operators on Lorentz sequence spaces (English) |
| Author:
|
Arora, S. C. |
| Author:
|
Datt, Gopal |
| Author:
|
Verma, Satish |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
87-98 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Description of multiplication operators generated by a sequence and composition operators induced by a partition on Lorentz sequence spaces $l(p,q)$, $1<p \le \infty $, $1\le q \le \infty $ is presented. (English) |
| Keyword:
|
composition operator |
| Keyword:
|
distribution function |
| Keyword:
|
Fredholm operator |
| Keyword:
|
Lorentz space |
| Keyword:
|
Lorentz sequence space |
| Keyword:
|
multiplication operator |
| Keyword:
|
non-increasing rearrangement |
| MSC:
|
46E30 |
| MSC:
|
47B33 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1211.47027 |
| idMR:
|
MR2504693 |
| DOI:
|
10.21136/MB.2009.140643 |
| . |
| Date available:
|
2010-07-20T17:50:09Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140643 |
| . |
| Reference:
|
[1] Abrahamse, M. B.: Multiplication Operators.Lecture Notes in Math., Vol. 693, Springer 17-36 (1978). Zbl 0411.47021, MR 0526530, 10.1007/BFb0064658 |
| Reference:
|
[2] Allen, G. D.: Duals of Lorentz spaces.Pacific J. Math. 77 287-291 (1978). Zbl 0362.46012, MR 0510924, 10.2140/pjm.1978.77.287 |
| Reference:
|
[3] Arora, S. C., Gopal Datt, Satish Verma: Composition operators on Lorentz spaces.Bull. Austral. Math. Soc. 76 205-214 (2007). MR 2353207, 10.1017/S0004972700039599 |
| Reference:
|
[4] Bennett, C., Sharpley, R.: Interpolation of Operators.Pure and Applied Math. Vol. 129, Academic Press Inc., New York (1988). Zbl 0647.46057, MR 0928802 |
| Reference:
|
[5] Cui, Y., Hudzik, H., Romesh Kumar, Maligranda, L.: Composition operators in Orlicz spaces.J. Austral. Math. Soc. 76 189-206 (2004). MR 2041244, 10.1017/S1446788700008892 |
| Reference:
|
[6] Hudzik, H., Rajeev Kumar, Romesh Kumar: Matrix multiplication operators on Banach function spaces.Proc. Indian Acad. Sci. (Math. Sci.) 116 71-81 (2006). MR 2210306, 10.1007/BF02829740 |
| Reference:
|
[7] Hudzik, H., Kaminska, A., Mastylo, M.: On the dual of Orlicz-Lorentz space.Proc. Amer. Math. Soc. 130 1645-1654 (2003). MR 1887011, 10.1090/S0002-9939-02-05997-X |
| Reference:
|
[8] Hunt, R. A.: On $L(p, q)$ spaces.L'Enseignment Math. 12 249-276 (1966). Zbl 0181.40301, MR 0223874 |
| Reference:
|
[9] Kaminska, A., Raynaud, Y.: Isomorphic $lp$-subspaces in Orlicz-Lorentz sequence spaces.Proc. Amer. Math. Soc. 134 2317-2327 (2006). MR 2213705, 10.1090/S0002-9939-06-08266-9 |
| Reference:
|
[10] Lorentz, G. G.: Some new functional spaces.Ann. Math. 51 37-55 (1950). Zbl 0035.35602, MR 0033449, 10.2307/1969496 |
| Reference:
|
[11] Lorentz, G. G.: On the theory of spaces $\Lambda $.Pacific J. Math. 1 411-429 (1951). Zbl 0043.11302, MR 0044740, 10.2140/pjm.1951.1.411 |
| Reference:
|
[12] Montgomery-Smith, S. J.: Orlicz-Lorentz Spaces, Proceedings of the Orlicz Memorial Conference.Oxford, Mississippi (1991). |
| Reference:
|
[13] Nakai, E.: Pointwise multipliers on the Lorentz spaces.Mem. Osaka Kyoiku Univ. III Natur. Sci. Appl. Sci. 45 1-7 (1996). MR 1448884 |
| Reference:
|
[14] Singh, R. K., Kumar, A.: Multiplication and composition operators with closed ranges.Bull. Aust. Math. Soc. 16 247-252 (1977). MR 0493495, 10.1017/S0004972700023261 |
| Reference:
|
[15] Singh, R. K., Manhas, J. S.: Composition Operators on Function Spaces.North Holland Math. Stud. 179, Elsevier Science Publications Amsterdem (1993). Zbl 0788.47021, MR 1246562 |
| Reference:
|
[16] Stein, Elias M., Guido Weiss: Introduction to Fourier Analysis on Euclidean Spaces.Princeton Math. Series, Vol. 32, Princeton Univ. Press, Princeton N.J. (1971). MR 0304972 |
| Reference:
|
[17] Takagi, H.: Fredholm weighted composition operators.Integral Equations Oper. Theory 16 267-276 (1933). MR 1205002, 10.1007/BF01358956 |
| . |
