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On Various Generalizations of Semi-\({\mathcal {A}}\)-Fredholm Operators

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Starting from the definition of \({\mathcal {A}}\)-Fredholm and semi-\({\mathcal {A}}\)-Fredholm operator on the standard module over a unital \(C^{*}\) algebra \({\mathcal {A}}\), introduced in Ivković (Banach J Math Anal 13(4):989–1016, 2019) and Mishchenko and Fomenko (Izv Akad Nauk SSSR Ser Mat 43:831–859, 1979), we construct various generalizations of these operators and obtain several results as an analogue or a generalization of the results in Berkani and Sarih (Glasg Math J 43(3):457–465, 2001. https://doi.org/10.1017/S0017089501030075), Berkani (Proc Am Math Soc 130(6):1717–1723, 2001), Djordjević (Proc Am Math Soc 130(1):81–84, 2001) and Yang (Trans Am Math Soc 216:313–326, 1976). Moreover, we also study non-adjointable semi-\({\mathcal {A}}\)-Fredholm operators as a natural continuation of the work in Irmatov and Mishchenko (J K-Theory 2:329–351, 2008. https://doi.org/10.1017/is008004001jkt034) on non-adjointable \({\mathcal {A}}\)-Fredholm operators and obtain an analogue or a generalization in this setting of the results in Ivković (Banach J Math Anal 13(4):989–1016, 2019; Ann Funct Anal, 2020. https://doi.org/10.1007/43034-019-00034-z).

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Acknowledgements

I am especially grateful to my supervisors Professor Vladimir M. Manuilov and Professor Camillo Trapani for reading my paper and for giving me comments that led to the improved presentation of the paper. Also, I am grateful to Professor Dragan S. Djordjevic for suggesting the research topic of this paper and for introducing to me the relevant reference books. Finally, I am grateful to the Referee for useful comments that led to the improved version of the paper.

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Correspondence to Stefan Ivković.

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Communicated by Daniel Aron Alpay.

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This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Aurelian Gheondea and Serap Oztop.

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Ivković, S. On Various Generalizations of Semi-\({\mathcal {A}}\)-Fredholm Operators. Complex Anal. Oper. Theory 14, 41 (2020). https://doi.org/10.1007/s11785-020-00995-3

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