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  • 1 Hasuda 518-4-301 Hasuda Saitama 349-0115 Japan Hasuda Saitama 349-0115 Japan
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Abstract  

Kaufman’s representation theorem is that a closed operator S with a dense domain in Hilbert space H is represented by a quotient S = B/(1 − B*B)1/2 for a unique contraction B. When S is a symmetric operator, what is a condition of the spectrum of B to admit selfadjoint extensions of S? In this note, it is shown that if there are no negative real points in the spectrum of B, then S has selfadjoint extensions.

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