On complementary subspaces of Hilbert space |
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Authors: | W E Longstaff Oreste Panaia |
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Institution: | Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6907, Australia ; Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6907, Australia |
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Abstract: | Every pair of non-trivial topologically complementary subspaces of a Hilbert space is unitarily equivalent to a pair of the form on a Hilbert space . Here is possibly , is a positive injective contraction and denotes the graph of . For such a pair the following are equivalent: (i) is similar to a pair in generic position; (ii) and have a common algebraic complement; (iii) is similar to for some operators on a Hilbert space. These conditions need not be satisfied. A second example is given (the first due to T. Kato), involving only compact operators, of a double triangle subspace lattice which is not similar to any operator double triangle. |
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Keywords: | |
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