Multiplication Operators On Grand Lorentz Spaces

Öz

In this paper, multiplication operators on grand Lorentz spaces are defined and the fundamental properties such as boundedness, closed range, invertibility, compactness and closedness of these are characterized.

Anahtar Kelimeler

• Grand Lorentz space,Multiplication operator,Compact operator

Büyük Lorentz Uzaylarında Çarpım Operatörleri

Öz

Bu çalışmada büyük Lorentz uzaylarında çarpım operatörleri tanımlandı ve sınırlılık, kapalı görüntü, terslenebilirlik, kompaktlık ve kapalılık gibi temel özellikleri karakterize edildi.

Anahtar Kelimeler

• Büyük Lorentz uzayları,Çarpım Operatörü,Kompakt(tıkız) operator

Kaynakça

1. Abrahamese, MB.1978. Multiplication Operators, Lecture Notes in Math. 693, Springer-Verlag, 17-36.
2. Adams,RA. and Fournier,JF. 2003. Sobolev Spaces, second edition, Pure and Applied Math. Series, 140, Academic press, New York.
3. Arora,SC., Datt,G. and Verma,S. 2006. Multiplication Operators on Lorentz Spaces, Indian Journal of Mathematics Vol. 48, No. 3, 317-329.
4. Arora,SC., Datt,G. and Verma,S. 2007a. Composition Operators on Lorentz Spaces, Bull. Austral. Math. Soc. Vol. 76, 205-214.
5. Arora,SC., Datt,G. and Verma,S. 2007b.Weighted Composition Operators on Lorentz Spaces, Bull. Korean Math. Soc. 44(4), 701-708.
6. Arora,SC., Datt,G. and Verma,S. 2008. Multiplication and Composition Operators on Lorentz Bochner Spaces, Osaka J. Math. 45(3), 629-641.
7. Bennett,C., Sharpley,R. 1988. Interpolation of operators, vol. 129, Pure and Applied Mathematics. Academic Press Inc., Boston, MA.
8. Carro,MJ., Martin,J. 2004. A useful estimate for the decreasing rearrangement of the sum of functions, Quart. J. Math., vol. 55, no.1, 41-45.

9. Day,PW. 1970. Rearrangements of measurable functions. ProQuest LLC, Ann Arbor, MI, Thesis (Ph.D.)-California Institute of Technology.
10. Halmos,PR. 1961. A Hilbert Space Problem Book, Van Nostrand Princeton, N.J.
11. Hardy,GH., Littlewood,JE. and Polya,G. 1952. Inequalities. Cambridge, at the University Press, second ed.
12. Hudzik, H., Kumar,R. and Kumar,R. 2006. Matrix multiplication operators on Banach function spaces, Proc. Indian Acad. Sci, (Math Sci.), 71-81.
13. Hunt, RA. 1964. An extension of Marcinkiéwicz interpolation theorem to Lorentz spaces. Bull. Am. Math. Soc., 70:803-807.
14. Hunt,RA. 1966. On L(p,q) spaces. Ensign. Math. (2), 12:249-276.
15. Komal,BS., Gupta,S. 2001. Multiplication operators between Orlicz spaces, Integral Equations and Operator Theory, 41, 324-330.
16. Köthe,G. 1969. Topological vector spaces I. Berlin-Heidelberg-New York: Springer Verlag, 15, 456 p.
17. Lorentz, GG. 1950. Some new function spaces, Ann. Math. 51(1), 37-55.
18. Lorentz, GG. 1951.On the theory of Spaces ,Pacific J. Math., 1, 411-429
19. Nakai,E. 1996. Pointwise multipliers on the Lorentz spaces, Mem. Osaka Kyoiku Univ., Natur. Sci. Appl. 45, No. 1, 1-7.
20. O’Neil,R. 1963. Convolution operators and L(p,q) spaces, Duke Math. J. 30,129-142
21. Singh,RK., Manhas,JS. 1993. Composition operators on function spaces, North Holland Math. Studies 179, Elsevier Science Publications Amsterdam, New York. Stein,EM., Weiss,G. 1971. Introduction to Fourier Analysis on Euclidean Spaces, Princeton N.J.
22. Takagi,H. 1993. Fredholm weighted composition operators, Integral Equations and Operators and Operator Theory, 16, 267-276.