عملگرهای ترکیبی و ضربی روی فضاهای اورلیچ

نویسندگان
گروه ریاضی، دانشگاه پیام نور
چکیده
عملگرهای ترکیبی تولید شده به‌وسیلۀ تبدیل خطی اندازه‌پذیر و غیرمنفرد و عملگر ضربی ، تولید شده به‌وسیلۀ تابع اندازه‌پذیر ، بین دو فضای متفاوت اورلیچ و را در نظر می‌گیریم. سپس کرانداری، فشردگی و نرم اساسی عملگرهای ترکیبی و ضربی را از نظر خواص تابع ، تابع و فضای اندازه بررسی می‌کنیم. در حقیقت تعدادی از نتایج [8]، [9]، [22] را توسیع می‌دهیم.
کلیدواژه‌ها

عنوان مقاله English

Composition Operators and Multiplication Operators on Orlicz Spaces

نویسندگان English

Y Estaremi
S Shamsi Gomechi
Payame Noor University

کلیدواژه‌ها English

Composition operator
Multiplication operator
compact operators
Orlicz spaces
essential norm
1. Abrahamse M.B., "Multiplication Operators, Lecture Notes in Mathematics", 693 (1978) 17-36. 2. Axler A., "Multiplication Operators on Bergman Spaces", J. Reine, Angew Math., 336 (1982) 26-44. 3. Arora S.C., "Gopal Datt and Satish Verma, Composition operators on Lorentz spaces", Bull., Austral, Math. Soc., 76 (2007) 205-214. 4. Douglas R.G., "Banach Algebra Techniques in Operator Theory", Academic Press, New York (1972). 5. Estaremi Y., Jabbarzadeh M.R., "Weighted lambert type operators on Lp-spaces", Oper. and Matrices, 7 (2013) 101-116. 6. Halmos P.R., "A Hilbert Space Problem Book, Van Nostr and Princeton", N.J. (1961). 7. H. Hudzik and M. Krbec, On non-effective weights in Orlicz spaces. Indag., Math. (N.S.) 18 (2007) 215-231. 8. Cui Y., Hudzik H., Kumar R., Maligranda L., "Composition operators in Orlicz spaces", J. Aust. Math. Soc., 76 (2004) 189-206. 9. Komal B.S., Gupta S., "Multiplication operators between Orlicz spaces", Integral equation and operator theory, 41 (2001) 324-330. 10. Kumar R., "ffComposition operators on Orliczspacesff", Integral Equations Operator Theory 29 (1997) 17ff22. 11. Musielak J., "Orlicz spaces and modular spaces", Lecture Notes in Math.1034 (Springer, Berlin (1983). 12. Lambert A., "Operator algebras related to measure preserving transformations of finite order", Rocky Mountain J. Math., 14 (1984) 341-349. 13. Rao M.M., "ffConvolutions of vector fieldsffII: random walk modelsff", Nonlinear Anal, Theory Methods Appl., 47 (2001) 3599-3615. 14. Raj K., Sharma S.K., Kumar A, "Multiplication operator on Musielak-Orlicz spaces", Advances and Applications in Mathmatical Sciences, 10 (2011) 473-480. 15. Montes-Rodr´ýguez A., "The essential norm of a composition operator on Bloch spaces", Pacific J. Math., 188 (1999) 339-351. 16. Singh R.K., Manhas J.S., "Composition operators on function spaces", North Holland Math., Studies 179, Amsterdam (1993). 17. Gupta S., Komal B.S, Suri N., "Weighted composition operators on Orlicz spaces", Int. J. Contemp, Math. Sciences, 1, (2010) 11-20. 18. Shapiro J.H., "The essential norm of a composition operator", Analls of Math., 125 (1987) 375-404. 19. Takagi H., "Compact weighted composition operators on Lp", Proc. Amer. Math. Soc., 116 (1992) 505-511. 20. Takagi H., "FredhoIm Weighted Composition Operators", Integral Equations and Operator Theory 16 (1993) 267-276. 21. Takagi T., Miura T., "Takahasi, Sin-Ei: Essential norm and stability constants of weighted composition operators on C(X)", Bull. Korean Math. Soc., 40, 583-591 (2003). 22. Takagi H., Yokouchi K., "Multiplication and composition operators between two Lp-spaces", Contemporary Math., 232 (1999) 321-338. 23. Zaanen A.C., "Integration, 2nd ed.", North-Holland, Amsterdam (1967). 24. Zheng L., "The essential norms and spectra of composition operators on H∞", Pacific J. Math., 203, 503-510 (2002).