On complementary subspaces of Hilbert space

Authors:
W. E. Longstaff and Oreste Panaia

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3019-3026

MSC (1991):
Primary 46C05

DOI:
https://doi.org/10.1090/S0002-9939-98-04547-X

MathSciNet review:
1468197

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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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Additional Information

**W. E. Longstaff**

Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6907, Australia

Email:
longstaff@maths.uwa.edu.au

**Oreste Panaia**

Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6907, Australia

Email:
oreste@maths.uwa.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-98-04547-X

Received by editor(s):
March 14, 1997

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society