Abstract
A typical result of this paper is the following: A closed linear operator T between Banach spaces X and Y is lower semi-Fredholm iff it is a rk-(=relatively compact)surjection, i.e. for every bounded sequence (yn) in Y there is a bounded sequence (xn) in D(T) such that (yn−Txn) is relatively compact in Y. The concept of co-(rk- and wk-)injections and surjections are introduced to characterize semi-Fredholm properties (in the usual or generalized sense). This is done also by new operator moduli.
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BERBERIAN, S.K.: Approximate proper values. Proc. Amer. Math. Soc.13, 111–114 (1962)
BUONI, J.J., HARTE, R.E. and WICKSTEAD, A.W.: Upper and lower Fredholm spectra. Proc. Amer. Math. Soc.66, 309–314 (1977)
BUONI, J.J., KLEIN,A.: On the generalized Calkin algebra. Pacific J. Math.80, 9–12 (1979)
CHADWICK, J.J.M., WICKSTEAD, A.W.: A quotient of ultrapowers of Banach spaces and semi-Fredholm operators. Bull. London Math. Soc.9, 321–325 (1977)
FÖRSTER, K.-H., LIEBETRAU, E.-O.: On semi-Fredholm operators and the conjugate of a product of operators. Studia Math.49, 301–306 (1977)
GINDLER, H.A., TAYLOR, A.E.: The minimal modulus of a linear operator and its use in spectral theory. Studia Math.22, 15–41 (1962)
GOLDBERG, S.: Unbounded linear operators. New York: McGraw-Hill 1966
HARTE, R.E.: Berberian-Quigley and the ghost of a spectral mapping theorem. Proc. R.I.A:78, 63–68 (1978)
HARTE, R.E., WICKSTEAD, A.W.: Upper and lower Fredholm spectra II. Math. Z.154, 253–256 (1977)
KAUFMAN, R.: Operators with closed range. Proc. Amer. Math. Soc.17, 767–768 (1966)
PIETSCH, A.: Operator ideals. Berlin: VEB Deutscher Verlag der Wissenschaften 1978
PRÖSSDORF, S.: Einige Klassen singulärer Gleichungen. Basel: Birkhäuser Verlag 1974
SADOVSKII, B.N.: Limit-compact and condensing operators. Russ. Math. Surveys27, 85–155 (1972)
YANG, K.-W.: The generalized Fredholm operators. Trans. Amer. Math. Soc.216, 313–326 (1976)
YANG, K.-W.: Operators invertible modulo the weakly compact operators. Pacific J. Math.71, 559–564 (1977)
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Förster, K.H., Liebetrau, E.O. Semi-Fredholm operators and sequence conditions. Manuscripta Math 44, 35–44 (1983). https://doi.org/10.1007/BF01166071
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DOI: https://doi.org/10.1007/BF01166071