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On Various Generalizations of Semi- $${\mathcal {A}}$$ A -Fredholm Operators
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2020-04-13 , DOI: 10.1007/s11785-020-00995-3
Stefan Ivković

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).

中文翻译:

关于半$$ {\ mathcal {A}} $$ A -Fredholm运算符的各种推广

\({\ mathcal {A}} \)- Fredholm和Semi- \({\ mathcal {A}} \)- Fredholm运算符的定义开始,在标准模块上的\(C ^ {*} \ )代数\({\ mathcal {A}} \),分别在Ivković(Banach J Math Anal 13(4):989–1016,2019)和Mishchenko和Fomenko(Izv Akad Nauk SSSR Ser Mat 43:831–859,1979)中引入,我们对这些算子进行了各种归纳并获得了几种结果作为Berkani和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)和Yang(Trans Am Math Soc 216:313–326,1976)。此外,我们还研究了非可连接的半\({{mathcal {A}} \)- Fredholm运算符,作为Irmatov和Mishchenko的工作的自然延续(J K-理论2:329-351,2008。https: //doi.org/10.1017/is008004001jkt034)在不可连接的\({\ mathcal {A}} \)上-Fredholm运算符,并在Ivković的这种结果设置中获得类似物或概括(Banach J Math Anal 13(4):989-1016,2019; Ann Funct Anal,2020. https://doi.org/10.1007/ 43034-019-00034-z)。
更新日期:2020-04-13
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