| Biography | |
|---|---|
 Prof. Salah Mecheri Tebessa University, Algeria |
|
| Title: Invariant and hyperinvariant subspaces problem for hyponormal operators | |
| Abstract: The question whether every operator on infinite dimensional Hilbert space H has a non-trivial invariant subspace or a non-trivial hyperinvariant subspace is one of the most difficult problem in operator theory. This problem is open for more than half a century. A subnormal operator has a non-trivial invariant subspace, but the existence of non-trivial invariant subspace for a hyponormal operator T still open. In this paper we give an affirmative answer of the existence of a non-trivial hyperinvariant subspace for a hyponormal operator. More generally, we show that a large classis of operators containing the class of hyponormal operators have non-trivial hyperinvariant subspaces. Finally, we show that every super-decomposable operator on a Banach space has a non-trivial hyperinvariant subspace. In particular, every generalized scalar operator, compact operator, and Riesz operator on a Banach space $X$ have non-trivial hyperinvariant subspaces. | |
| Biography: Dr. Salah Mecheri is a Professor of Mathematics. His research is mostly in Functional Analysis. In particular, Operator theory and Spectral theory. He has authored more than 100 publications in international journals, including two books in French and a chapter in a monograph, referee for more than 20 international journals and was the supervisor of 08 PhD students. Salah Mecheri is currently a member of the editorial board of two international journals. He has gotten many research funds since he got a doctorate in 1999. He was honored Award for Research Excellence in King Saud University and at Taibah university. | |
