Abstract.
We present an alternative proof of a characterization, due to M. Lauzon and S. Treil, of subspaces with a common complement in a separable Hilbert space. Our approach is motivated by known results concerning the relative position of two subspaces in a Hilbert space. As byproducts we obtain a simple example of a double triangle subspace lattice which is not similar to an operator double triangle and a characterization of pairs of subspaces in generic position which are not completely asymptotic to one another.
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Drivaliaris, D., Yannakakis, N. Subspaces with a Common Complement in a Separable Hilbert Space. Integr. equ. oper. theory 62, 159–167 (2008). https://doi.org/10.1007/s00020-008-1622-5
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DOI: https://doi.org/10.1007/s00020-008-1622-5
Keywords.
- Common complement
- algebraic complement
- pair of subspaces
- relative position
- generic position
- equivalently positioned subspaces
- completely asymptotic subspaces
- Hilbert space geometry
- double triangle subspace lattice