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Compact and Finite Rank Perturbations of Closed Linear Operators and Relations in Hilbert Spaces |
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| Authors: | Tomas Ya. Azizov Jussi Behrndt Peter Jonas Carsten Trunk |
| Affiliation: | 1. Department of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394006, Voronezh, Russia 2. Institut für Mathematik, MA 6-4,, Technische Universit?t Berlin, Stra?e des 17. Juni 136, 10623, Berlin, Germany 3. Institut für Mathematik, Technische Universit?t Ilmenau, Postfach 10 05 65, 98684, Ilmenau, Germany |
| Abstract: | For closed linear operators or relations A and B acting between Hilbert spaces  and  the concepts of compact and finite rank perturbations are defined with the help of the orthogonal projections P A and P B in  onto the graphs of A and B. Various equivalent characterizations for such perturbations are proved and it is shown that these notions are a natural generalization of the usual concepts of compact and finite rank perturbations. Sadly, our colleague and friend Peter Jonas passed away on July, 18th 2007. |
| Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 47A55 Secondary 47A06 |
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