Advances in Operator Theory

Operators with compatible ranges in an algebra generated by two orthogonal projections

Ilya M Spitkovsky

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The criterion is obtained for operators $A$ from the algebra generated by two orthogonal projections $P,Q$ to have a compatible range, i.e., coincide with the hermitian conjugate of $A$ on the orthogonal complement to the sum of their kernels. In the particular case of $A$ being a polynomial in $P,Q$, some easily verifiable conditions are derived.

Article information

Adv. Oper. Theory, Volume 3, Number 1 (2018), 117-122.

Received: 2 February 2017
Accepted: 25 April 2017
First available in Project Euclid: 5 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
Secondary: 47C15: Operators in $C^*$- or von Neumann algebras 47L30: Abstract operator algebras on Hilbert spaces

Hermitian operators orthogonal projections von Neumann algebras


Spitkovsky, Ilya M. Operators with compatible ranges in an algebra generated by two orthogonal projections. Adv. Oper. Theory 3 (2018), no. 1, 117--122. doi:10.22034/aot.1702-1111.

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