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In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order $\alpha $ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.
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참고문헌 (18)
참고문헌 신청
W. Y. Akashi / 1984 / On the perturbation theory for Fredholm operators / Osaka J. Math. 21(3):603~612
A. Ammar / 2014 / Stability of the S-left and S-right essential spectra of a linear operator / Acta Math. Sci. Ser. B (Engl. Ed.) 34(6):1922~1934
F. V. Atkinson / 1994 / The essential spectrum of some matrix operators / Math. Nachr. 167:5~20
A. Batkai / 2005 / Spectral problems for operator matrices / Math. Nachr. 278(12-13):1408~1429
W. Chaker / 2015 / Demicompact linear operators, essential spectrum and some perturbation results / Math. Nachr. 288(13):1476~1486
A. Ammar / 2014 / Stability of the S-left and S-right essential spectra of a linear operator / Acta Math. Sci. Ser. B (Engl. Ed.) 34(6):1922~1934
F. V. Atkinson / 1994 / The essential spectrum of some matrix operators / Math. Nachr. 167:5~20
A. Batkai / 2005 / Spectral problems for operator matrices / Math. Nachr. 278(12-13):1408~1429
W. Chaker / 2015 / Demicompact linear operators, essential spectrum and some perturbation results / Math. Nachr. 288(13):1476~1486
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