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In this paper, we show that an unbounded $S_{0}$-demicompact linear operator $T$ with respect to a bounded linear operator $S_{0}$, acting on a Banach space, can be characterized by the Kuratowskii measure of noncompactness. Moreover, some other quantities related to this measure provide sufficient conditions to the operator $T$ to be $S_{0}$-demicompact. The obtained results are used to discuss the connection with Fredholm and upper Semi-Fredholm operators.
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참고문헌 (20)
참고문헌 신청
P. Aiena / 2007 / Semi-Fredholm operators, perturbation theory and localized SVEP
W. Y. Akashi / 1984 / On the perturbation theory for Fredholm operators / Osaka J. Math. 21(3):603~612
J. Appell / 2005 / Measures of noncompactness, condensing operators and fixed points: an application-oriented survey / Fixed Point Theory 6(2):157~229
K. Astala / 1980 / On measures of noncompactness and ideal variations in Banach spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes No. 29 :42
S. Axler / 1980 / The essential norm of an operator and its adjoint / Trans. Amer. Math. Soc. 261(1):159~167
W. Y. Akashi / 1984 / On the perturbation theory for Fredholm operators / Osaka J. Math. 21(3):603~612
J. Appell / 2005 / Measures of noncompactness, condensing operators and fixed points: an application-oriented survey / Fixed Point Theory 6(2):157~229
K. Astala / 1980 / On measures of noncompactness and ideal variations in Banach spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes No. 29 :42
S. Axler / 1980 / The essential norm of an operator and its adjoint / Trans. Amer. Math. Soc. 261(1):159~167
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