Advances in Operator Theory

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

Ilya M Spitkovsky

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512497955

Digital Object Identifier
doi:10.22034/aot.1702-1111

Mathematical Reviews number (MathSciNet)
MR3730342

Zentralblatt MATH identifier
06804319

Subjects
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

Keywords
Hermitian operators orthogonal projections von Neumann algebras

Citation

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


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References

  • A. B öttcher and I. M. Spitkovsky, A gentle guide to the basics of two projections theory, Linear Algebra Appl. 432 (2010), no. 6, 1412–1459.
  • M. S. Djikić, Operators with compatible ranges, arXiv.math.FA/1609.04884v1.
  • R. Giles and H. Kummer, A matrix representation of a pair of projections in a Hilbert space, Canad. Math. Bull. 14 (1971), no. 1, 35–44.
  • P. L. Halmos, Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381–389.
  • I. M. Spitkovsky, Once more on algebras generated by two projections, Linear Algebra Appl. 208/209 (1994), 377–395.
  • ––––, On polynomials in two projections, Electron. J. Linear Algebra 15 (2006), 154–158.