Not all pure states on B(H) are diagonalizable

Charles Akemann; Nik Weaver

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Not all pure states on B(H) are diagonalizable

Charles Akemann·Nik Weaver

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Abstract

Assuming the continuum hypothesis, we prove that B(H) has a pure state whose restriction to any masa is not pure. This resolves negatively an old conjecture of Anderson.

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Charles Akemann, Nik Weaver. 2006-06-07. Not all pure states on B(H) are diagonalizable. https://arxiv.org/abs/math/0606168

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