In this paper,
it is aimed to find necessary conditions for any operator defined on Lebesgue
spaces to be a composition operator. Also some properties of these operators
will be examined.
References
Bartle R. G. (2014). The elements of integration and Lebesgue measure. John Wiley & Sons,
Boyd D. M. (1974). Composition operators on the Bergman space and analytic function spaces on the annulus. University of North Carolina at Chapel Hill.
Caughran J. G. and Halmos P. (1971). Polynomial approximation and spectral properties of composition operators on H 2. Indiana University Mathematics Journal, 21(1): 81-84.
Caughran J. G. and Schwartz H. J. (1975). Spectra of compact composition operators. Proceedings of the American Mathematical Society, 51(1): 127-130.
Choksi J. (1966). Unitary operators induced by measure preserving transformations. Journal of Mathematics and Mechanics, 16(1): 83-100.
Cima J. and Wogen W. (1974). On algebras generated by composition operators. Canad. J. Math, 26: 1234-1241.
Cima J. A., Thomson J. and Wogen W. (1974). On some properties of composition operators. Indiana University Mathematics Journal, 24(3): 215-220.
Halmos P. R. (1956). Lectures on ergodic theory. American Mathematical Soc.
Halmos P. R. and von Neumann J (1942). Operator methods in classical mechanics, II. Annals of Mathematics: 332-350.
Harrington, D. J. and Whitley, R. (1984). Seminormal composition operators. Journal of Operator Theory, 125-135.
Johnson R. A. (1970). Atomic and nonatomic measures. Proceedings of the American Mathematical Society, 25(3): 650-655.
Kamowitz H. (1981). Compact weighted endomorphisms of Proceedings of the American Mathematical Society, 83(3): 517-521.
Kızmaz H. (1993). Fonksiyonel Analize Giriş. Karadeniz Teknik Üniversitesi Basımevi, Trabzon.
Koopman B. and Neumann J. v (1932). Dynamical systems of continuous spectra. Proceedings of the National Academy of Sciences, 18(3): 255-263.
Koopman B. O. (1931). Hamiltonian systems and transformation in Hilbert space. Proceedings of the National Academy of Sciences, 17(5): 315-318.
Littlewood J. E. (1925). On inequalities in the theory of functions. Proceedings of the London Mathematical Society, 2(1): 481-519.
Nordgren E. A. (1968). Composition operators. Canad. J. Math, 20: 442-449.
Nordgren E. A. (1978). Hilbert space operators. Springer, 37-63.
Rudin W. (1987). Real and complex analysis. Tata McGraw-Hill Education,
Rynne B. P. and Youngson M. A. (2000). Linear functional analysis. Springer Science and Business Media,
Singh, R. K. (1975). Normal and Hermitian composition operators. Proceedings of the American Mathematical Society, 47(2), 348-350.
Singh, R. K. (1976a). Composition operators induced by rational functions. Proceedings of the American Mathematical Society, 59(2), 329-333.
Singh R.K. (1976b). İnvertible composition operators on . Proceedings of the American Mathematical Society, 56: 1, 127-129.
Singh, R. K. and Kumar, A. (1977). Multiplication operators and composition operators with closed ranges. Bull. Austral. Math. Soc, 16, 247-252.
Singh, R. K., and Kumar, A. (1978). Characterizations of invertible, unitary, and normal composition operators. Bulletin of the Australian Mathematical Society, 19(1), 81-95.
Singh, R. K. and Kumar, A. (1979). Compact composition operators. Journal of the Australian Mathematical Society, 28(3), 309-314.
Singh R. K. and Manhas J S (1993). Composition operators on function spaces, North-Holland Mathematics Studies, 179.
Bu çalışmada Lebesgue uzayları üzerinde tanımlı bir
operatörün bileşke operatör olması için gerekli şartlar ve bileşke
operatörlerinin sağladığı bazı özelliklerin gösterilmesi amaçlanmaktadır.
Bartle R. G. (2014). The elements of integration and Lebesgue measure. John Wiley & Sons,
Boyd D. M. (1974). Composition operators on the Bergman space and analytic function spaces on the annulus. University of North Carolina at Chapel Hill.
Caughran J. G. and Halmos P. (1971). Polynomial approximation and spectral properties of composition operators on H 2. Indiana University Mathematics Journal, 21(1): 81-84.
Caughran J. G. and Schwartz H. J. (1975). Spectra of compact composition operators. Proceedings of the American Mathematical Society, 51(1): 127-130.
Choksi J. (1966). Unitary operators induced by measure preserving transformations. Journal of Mathematics and Mechanics, 16(1): 83-100.
Cima J. and Wogen W. (1974). On algebras generated by composition operators. Canad. J. Math, 26: 1234-1241.
Cima J. A., Thomson J. and Wogen W. (1974). On some properties of composition operators. Indiana University Mathematics Journal, 24(3): 215-220.
Halmos P. R. (1956). Lectures on ergodic theory. American Mathematical Soc.
Halmos P. R. and von Neumann J (1942). Operator methods in classical mechanics, II. Annals of Mathematics: 332-350.
Harrington, D. J. and Whitley, R. (1984). Seminormal composition operators. Journal of Operator Theory, 125-135.
Johnson R. A. (1970). Atomic and nonatomic measures. Proceedings of the American Mathematical Society, 25(3): 650-655.
Kamowitz H. (1981). Compact weighted endomorphisms of Proceedings of the American Mathematical Society, 83(3): 517-521.
Kızmaz H. (1993). Fonksiyonel Analize Giriş. Karadeniz Teknik Üniversitesi Basımevi, Trabzon.
Koopman B. and Neumann J. v (1932). Dynamical systems of continuous spectra. Proceedings of the National Academy of Sciences, 18(3): 255-263.
Koopman B. O. (1931). Hamiltonian systems and transformation in Hilbert space. Proceedings of the National Academy of Sciences, 17(5): 315-318.
Littlewood J. E. (1925). On inequalities in the theory of functions. Proceedings of the London Mathematical Society, 2(1): 481-519.
Nordgren E. A. (1968). Composition operators. Canad. J. Math, 20: 442-449.
Nordgren E. A. (1978). Hilbert space operators. Springer, 37-63.
Rudin W. (1987). Real and complex analysis. Tata McGraw-Hill Education,
Rynne B. P. and Youngson M. A. (2000). Linear functional analysis. Springer Science and Business Media,
Singh, R. K. (1975). Normal and Hermitian composition operators. Proceedings of the American Mathematical Society, 47(2), 348-350.
Singh, R. K. (1976a). Composition operators induced by rational functions. Proceedings of the American Mathematical Society, 59(2), 329-333.
Singh R.K. (1976b). İnvertible composition operators on . Proceedings of the American Mathematical Society, 56: 1, 127-129.
Singh, R. K. and Kumar, A. (1977). Multiplication operators and composition operators with closed ranges. Bull. Austral. Math. Soc, 16, 247-252.
Singh, R. K., and Kumar, A. (1978). Characterizations of invertible, unitary, and normal composition operators. Bulletin of the Australian Mathematical Society, 19(1), 81-95.
Singh, R. K. and Kumar, A. (1979). Compact composition operators. Journal of the Australian Mathematical Society, 28(3), 309-314.
Singh R. K. and Manhas J S (1993). Composition operators on function spaces, North-Holland Mathematics Studies, 179.
Eryılmaz, İ., & Değirmen, İ. (2019). Lebesgue Uzayları Üzerinde Bileşke Operatörler. Erzincan University Journal of Science and Technology, 12(2), 533-542. https://doi.org/10.18185/erzifbed.421048