Orlicz-Lorentz Spaces and their Composition Operators

René Erlin Castillo

Universidad Nacional de Colombia, Colombia 

Héctor Camilo Chaparro 

Universidad Nacional de Colombia, Colombia 

Julio César Ramos Fernández

Universidad de Oriente, Venezuela 

---

ABSTRACT

In a self-contained presentation, we discuss the Orlicz-Lorentz space. Also the boundedness of composition operators on Orlicz-Lorentz spaces are characterized in this paper.

2010 Mathematics Subject Clasification : Primary 47B33, 47B38, secondary 46E30.

---

REFERENCES

[1]    M. B. Abrahamese, Multiplication operators, Lecture notes in Math., Vol. 693, pp. 17-36, Springer Verlag, New York, (1978).         [ Links ]

[2]    Y. A. Abramovich, C. D. Aliprantis, An Invitation to Operator Theory, American Mathematical Society, (2002).         [ Links ]

[3]    S.C Arora, Gopal Datt and Satish Verma, Multiplication operators on lorentz spaces, Indian Journal of Mathematics, Vol. 48, (3), pp. 317-329, (2006).         [ Links ]

[4]    A. Axler, Multiplication operators on Bergman space, J. Peine Angew Math., Vol. 33 (6), pp. 26-44, (1982).         [ Links ]

[5]    Grafakos, Loukas. Classical Fourier Analysis Second Edition, Springer, (2008).         [ Links ]

[6]    R. E. Castillo, R. Leon; E. Trousselot. Multiplication operator on L(p,q) spaces, Panamer. Math Journal Vol. 19, No. 1, pp. 37-44, (2009).         [ Links ]

[7]    Y. Cui, H. Hudzik, Romesh Kumar and L. Maligranda, Composition operators in Orlicz spaces, J. Austral. Math. Soc., Vol. 76 (2), pp. 189-206, (2004).         [ Links ]

[8]    H. Hudzik, A. Kaminska and M. Mastylo, On the dual of Orlicz-Lorentz space, Proc. Amer. Math. Soc., Vol. 130 (6), pp. 1645-1654, (2003).         [ Links ]

[9]    B. S. Komal and Shally Gupta, Multiplication operators between Or-licz spaces, Integral Equations and Operator Theory. Vol. 41, pp. 324330, (2001).         [ Links ]

[10]    Romesh Kumar, Composition operators on Orlicz spaces, Integral Equations and Operator Theory. Vol. 29, pp. 17-22, (1997).         [ Links ]

[11]    Rajeev Kumar and Romesh Kumar, Compact composition operators on Lorentz spaces, Math. Vesnik, Vol. 57, pp. 109-112, (2005).         [ Links ]

[12]    E. Nordgren, Composition operators on Hilbert spaces, Lecture notes in Math., Vol. 693, pp. 37-68, Springer Verlag, New York, (1978).         [ Links ]

[13]    M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker Inc., New York, (1993).         [ Links ]

[14]    R. K. Singh and A. Kumar, Multiplication and composition operators with closed ranges, Bull. Aust. Math. Soc. Vol. 16, pp. 247-252, (1977).         [ Links ]

[15]    R. K. Singh and J. S. Manhas, Composition operators on Function Spaces, North Holland Math. Stud. Vol. 179, Elsevier Science Publications, Amsterdem, New York, (1993).         [ Links ]

René Erlin Castillo

Departamento de Matemáticas, Universidad Nacional de Colombia, Bogota,

Colombia

e-mail : recastillo@unal.edu.co

Héctor Camilo Chaparro

Departamento de Matemaáticas, Universidad Nacional de Colombia, Bogota,

Colombia

e-mail : hcchaparrog@unal.edu.co

Julio César Ramos Fernandez

Departamento de Matemaáticas Universidad de Oriente,

Cumana, Estado Sucre,

Venezuela

e-mail : jcramos@udo.edu.ve

Received : November 2012. Accepted : March 2014