On Various Generalizations of Semi-A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document}-Fredholm Operators

被引：0
作者：
Stefan Ivković
机构：
[1] The Mathematical Institute of the Serbian Academy of Sciences and Arts,
来源：
Complex Analysis and Operator Theory | 2020年 / 14卷 / 3期
关键词：
Generalized ; -Fredholm operator; Generalized ; -Weyl operator; Semi-; -; -Fredholm operator; Non-adjointable semi-; -Fredholm operator; Primary 47A53; Secondary 46L08;
D O I：
10.1007/s11785-020-00995-3
中图分类号：
学科分类号：
摘要：
Starting from the definition of A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document}-Fredholm and semi-A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document}-Fredholm operator on the standard module over a unital C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{*}$$\end{document} algebra A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document}, 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-A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document}-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 A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document}-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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