Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 1 (2018), 117-122.
Operators with compatible ranges in an algebra generated by two orthogonal projections
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.
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
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.aot/1512497955