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The many proofs of an identity on the norm of oblique projections. (English) Zbl 1102.47002
Summary: Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P 2 =P, which is neither null nor the identity, it holds that P=I-P. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.
MSC:
47A05General theory of linear operators
15A24Matrix equations and identities
15A60Applications of functional analysis to matrix theory
46C99Inner product spaces, Hilbert spaces
46E99Linear function spaces and their duals
46N40Applications of functional analysis in numerical analysis
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