Journal article
AN OPERATOR EQUATION, KDV EQUATION AND INVARIANT SUBSPACES
Proceedings of the American Mathematical Society, v 138(2), pp 717-724
01 Feb 2010
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Abstract
Let A be a bounded linear operator on a complex Banach space X. A problem, motivated by the operator method used to solve integrable systems such as the Korteweg-deVries (KdV), modified KdV, sine-Gordon, and Kadomtsev-Petviashvili (KP) equations, is whether there exists a bounded linear operator B such that (i) AB+BA is of rank one, and (ii) (I + f(A)B) is invertible for every function f analytic in a neighborhood of the spectrum of A. We investigate solutions to this problem and discover an intriguing connection to the invariant subspace problem. Under the assumption that the convex hull of the spectrum of A does not contain 0, we show that there exists a solution B to (i) and (ii) if and only if A has a non-trivial invariant subspace.
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Details
- Title
- AN OPERATOR EQUATION, KDV EQUATION AND INVARIANT SUBSPACES
- Creators
- R. V. Garimella - University of Central ArkansasV. Hrynkiv - University of Houston - DowntownA. R. Sourour - University of Victoria
- Publication Details
- Proceedings of the American Mathematical Society, v 138(2), pp 717-724
- Publisher
- Amer Mathematical Soc
- Number of pages
- 8
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000274739400034
- Scopus ID
- 2-s2.0-77951472186
- Other Identifier
- 991021862272904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied