The essential norm of multiplication operators acting on Orlicz sequence spaces

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-06-0086

Keywords:

Multiplication operator, Orlicz sequence spaces, Banach lattice, Essential norm

Abstract

We calculate the measure of non-compactness or the essential norm of the multiplication operator Mu acting on Orlicz sequence spaces lϕ. As a consequence of our result, we obtain a known criteria for the compactness of multiplication operator acting on lϕ.

Author Biographies

Julio César Ramos-Fernández, Universidad Distrital Francisco José de Caldas.

Facultad Tecnológica.

Margot Salas-Brown, Universidad del Rosario.

Escuela de Ingeniería, Ciencia y Tecnología, Matemáticas Aplicadas y Ciencias de la Computación.

References

S. C. Arora, G. Datt, and S. Verma, “Operators on Lorentz sequence spaces”, Mathematica bohemica, vol. 134, no. 1, pp. 87–98, 2009. [On line]. Available: https://bit.ly/31H7Chq

P. Bala, A. Gupta and N. Bhatia, “Multiplication operators on Orlicz-Lorentz sequence spaces”, International journal of mathematical analysis, vol. 7, no. 29-32, pp. 1461-1469, 2013, doi: 10.12988/ijma.2013.3360

R. E. Castillo, H. Rafeiro, J. C. Ramos-Fernández, and M. Salas-Brown, “Multiplication operator on Köthe spaces: measure of non-compactness and closed range”, Bulletin Malaysian Mathematics Sciences Society, vol. 42, no. 4, pp. 1523-1534, Jul. 2019, doi: 10.1007/s40840-017-0562-0

R. E. Castillo, J. C. Ramos-Fernández, and M. Salas-Brown, “The essential norm of multiplication operators on Lorentz sequence spaces”, Real analysis exchange, vol. 41, no. 1, pp. 245-251, 2016. [On line]. Available: https://bit.ly/35yrV1L

H. Hudzik, R. Kumar, and R. Kumar, “Matrix multiplication operators on Banach function spaces”, Proceedings of the Indian Academy of Sciences - Mathematical Science, vol. 116, no. 1, pp. 71-81, Feb. 2006, doi: 10.1007/BF02829740

L. V. Kantorovich and G. P. Akilov, Functional analysis, 2nd ed. Moscow: Nauka, 1977.

B. S. Komal, S. Pandoh, and K. Raj, “Multiplication operators on Cesàro sequence spaces”, Demonstratio mathematica, vol. 49, no. 4, pp. 430-436, Nov. 2016, doi: 10.1515/dema-2016-0037

P. Lin, Köthe-Bochner function spaces, Boston, MA: Birkhäuser, 2004.

K. Raj, C. Sharma, and S. Pandoh, “Multiplication operators on Cesàro-Orlicz sequence spaces”, Fasciculi mathematici, vol. 57, no. 1, pp. 137-145, 2016, doi: 10.1515/fascmath-2016-0021

J. C. Ramos-Fernández and M. Salas-Brown, “On multiplication operators acting on Köthe sequence spaces”, Afrika matematika, vol. 28, no. 3-4, pp. 661-667, Jun. 2017, doi: 10.1007/s13370-016-0475-3

M. M. Rao and Z. D. Ren, The theory of Orlicz spaces, New York, NY: Marcel Dekker, 1991.

R. K. Singh and A. Kumar, “Multiplication operators and composition operators with closed ranges”, Bulletin Australian Mathematical Society, vol. 16, no. 2, pp. 247-252, Apr. 1977, doi: 10.1017/S0004972700023261

R. K. Singh and A. Kumar, “Compact composition operators”, Journal of the Australian Mathematical Society. Series A. Pure Mathematics, vol. 28, no. 3, pp. 309-314, Nov. 1979, doi:10.1017/S1446788700012258

Published

2020-11-12

How to Cite

[1]
J. C. Ramos-Fernández and M. Salas-Brown, “The essential norm of multiplication operators acting on Orlicz sequence spaces”, Proyecciones (Antofagasta, On line), vol. 39, no. 6, pp. 1407-1414, Nov. 2020.

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Artículos