Title：Generalized inverses, matrix and operator equations V: Different classes of solutions of certain matrix and operator equations

Abstract：We will consider necessary and sufficient conditions for the existence of different classes of the solutions of certain matrix and operator equations. What was the motivation for this lecture? The principal motivation was the rather surprising fact that the necessary and sufficient conditions for the existence of a positive solution of the operator equation AXB=C are unknown in the general case. The existence of a positive solution of the equation AXB = C was considered in different settings but only under additional conditions including that of regularity, as well as under certain range conditions such as R(B) ⊆ R(A*). In this lecture we will consider this open question and present some equivalents of the existence of a positive solution of the operator equation AXB = C without any additional range assumptions, using a completely new technique that includes two well-known results of Douglas and Sebesty´en. Also we will consider a general form of a positive solution.

Speaker：Dragana S. Cvetković-Ilić，Department of Mathematics, Faculty of Science and Mathematics, University of Nis, Serbia

Dragana S. Cvetković-Ilić is a full professor of University of Nis, Serbia. Her main research field is the theory of generalized inverse and its applications. She has published more than 80 papers in SCI journals such as Linear Algebra Appl.，Proc. Amer. Math. Soc.，Linear & Multilinear Algebra，J. Austra. Math. Soc.，Acta Math. Sci.，Appl. Math. Comp.，J. Operator Theory and so on. She is a member of the Board of Directors of ILAS(International Linear Algebra Society), (3/2020-), member of the Editorial Board for the following journals: Journal of Computational and Applied Mathematics, Annals of Functional Analysis, FILOMAT, and FACTA UNIVERSITATIS, Series Mathematics and Informatics (Editor in Chief). She is also awarded by “For women in Sciences”, Loreal-Unesco, Serbia, and Award for achievements in Mathematical Sciences, Mathematical Society of Serbia.

Date：3:00pm-4:30pm 2021-4-30（Friday）.

Venue:

Tencent Meeting ID：637 883 920

Organizer：School of Mathematical Sciences

Students and teachers who are interested  are welcome.