Singular value estimates of oblique projections

✍ Scribed by Jorge Antezana; Gustavo Corach

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 140 KB
• Volume: 430
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.08.001

✦ Synopsis

Let W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M ⊥ , and let P W M ⊥ denote the oblique projection with range W and nullspace M ⊥ . In this article we get the following formula for the singular values of P W M ⊥ :

where the minimum is taken over the set of all operator pairs (F, H ) on H such that R(F ) = W, R(H ) = M and F H * = P W M ⊥ , and k ∈ {1, . . . , dim W}. We also characterize all the pairs where the minimum is attained.