We consider von Neumann algebras generated by two arbitrary orthoprojections on a Hilbert space. A canonical decomposition is obtained for elements A of these algebras in terms of the operator angle between the ranges of the above-mentioned projections. This decomposition leads to explicit descriptions and formulas for kernels, ranges, spectra and essential spectra, (generalized) inverses, and other objects related to A.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics