The product of operators with closed range in Hilbert C-modules |
| |
| Authors: | K. Sharifi |
| |
| Affiliation: | Department of Mathematics, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran |
| |
| Abstract: | Suppose T and S are bounded adjointable operators with close range between Hilbert C∗-modules, then TS has closed range if and only if Ker(T)+Ran(S) is an orthogonal summand, if and only if Ker(S∗)+Ran(T∗) is an orthogonal summand. Moreover, if the Dixmier (or minimal) angle between Ran(S) and Ker(T)∩[Ker(T)∩Ran(S)]⊥ is positive and  is an orthogonal summand then TS has closed range. |
| |
| Keywords: | Primary: 47A05 Secondary: 15A09, 46L08, 46L05 |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
