Idempotents in a space with conjugation

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Abstract

Let H be a complex Hilbert space with conjugation operator J. We study J-real operators and we have covered J-regular subspaces. We prove that for given bounded idempotent p there exists a conjugation operator J0 such that p is a J0-projection, i.e. p=J0pJ0.

AMS classification

28A60
46C20
46C50
47A63
47B50

Keywords

Hilbert space
Conjugation
Idempotent
Projection

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