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Contractive projections on Banach space

Published online by Cambridge University Press:  17 April 2009

Mark Spivack
Mark Spivack
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom
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Abstract

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In this note we prove the uniqueness of a projection onto a given subspace with strictly contractive complement. We also show that, if one completely contractive projection is invariant under another, then the two commute.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 271 - 274
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Arveson, W.B., “Operator algebras and invariant subspaces”, Ann. Math. 100 (1974) 433–532.CrossRefGoogle Scholar
[2]Cheney, E.W. and Price, K.M., “Minimal Projections”, in Approximation Theory, Ed. Talbot, A., (Academic Press, New York, 1970).Google Scholar
[3]Davidson, K.R., “Commutative subspace lattices”, Indiana Univ. Math. J. 27 (1978) 479–490.CrossRefGoogle Scholar
[4]Kakutani, S. and Mackey, G.W., “Ring and lattice characterisations of complex Hilbert space”, Bull. Amer. Math. Soc. 52 (1946) 727–733.CrossRefGoogle Scholar
d[5]Spivack, M., “Derivations and nest algebras on Banach space”, Israel J. Math. 50 (1985) 193–200.CrossRefGoogle Scholar