Abstract
Let Ф be a conditional expectation operator defined on a selfadjoint algebra of operators on a Hilbert space H. Let A be an invertible operator on Н, and let M be a subspaçe of H. A sufficient condition for M to be invariant for Ф (А-1)•A is obtained. A generalization involving sequences of conditional expectations yields a simplified and conceptually different proof of a recent theorem about operator factorization with respect to commutative sets of projections. It also provides a step toward the solution of the difficult problem of operator factorization with respect to noncommutative sets of projections.
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© 1988 Birkhäuser Verlag Basel
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Daughtry, J. (1988). Conditional Expectations and Invariant Subspaces. In: Gohberg, I., Helton, J.W., Rodman, L. (eds) Contributions to Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 35. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9284-1_2
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DOI: https://doi.org/10.1007/978-3-0348-9284-1_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9978-9
Online ISBN: 978-3-0348-9284-1
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