The structure of a real linear combination of two projections |
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Authors: | Katsuyoshi Nishio |
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Institution: | Department of Applied Mathematics Faculty of Engineering Ibaraki University Hitachi, Ibaraki 316, Japan |
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Abstract: | A necessary and sufficient condition for a Hermitian operator on a Hilbert space to be expressed as aP + bQ with some projections P, Q and reals a, b is established. Moreover the spectrum of such an operator is explicitly drawn in terms of the spectrum of PQ ∣ran P, the restriction to the range of P. |
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