The Angle Between Subspaces of a Hilbert Space

@inproceedings{Deutsch1995TheAB,
  title={The Angle Between Subspaces of a Hilbert Space},
  author={Frank Deutsch},
  year={1995}
}
This is a mainly expository paper concerning two different definitions of the angle between a pair of subspaces of a Hilbert space, certain basic results which hold for these angles, and a few of the many applications of these notions. The latter include the rate of convergence of the method of cyclic projections, existence and uniqueness of abstract splines, and the product of operators with closed range. 
The rate of convergence in the method of alternating projections
A generalization of the cosine of the Friedrichs angle between two subspaces to a parameter associated to several closed subspaces of a Hilbert space is given. This parameter is used to analyze the
When is the sum of closed subspaces of a Hilbert space closed
We provide a sufficient condition for a finite number of closed subspaces of a Hilbert space to be linearly independent and their sum to be closed. Under this condition a formula for the orthogonal
A classification of projectors
A positive operator A and a closed subspace S of a Hilbert space H are called compatible if there exists a projector Q onto S such that AQ = Q∗A. Compatibility is shown to depend on the existence of
On the angle and the minimal angle between subspaces
We study those pairs of subspaces of a complex Hilbert space with the same angle and minimal angle and present several characterizations of the pairs of subspaces with angle equal to .
Projections in operator ranges
If H is a Hilbert space, A is a positive bounded linear operator on H and S is a closed subspace of H, the relative position between S and A -1 (S⊥) establishes a notion of compatibility. We show
On the Reduced Minimum Modulus of Projections and the Angle between Two Subspaces
Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N , respectively. In this note, an exact representation of the angle and the minimum
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