English

Not all pure states on B(H) are diagonalizable

Operator Algebras 2007-05-23 v1 Functional Analysis Logic

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.

Cite

@article{arxiv.math/0606168,
  title  = {Not all pure states on B(H) are diagonalizable},
  author = {Charles Akemann and Nik Weaver},
  journal= {arXiv preprint arXiv:math/0606168},
  year   = {2007}
}

Comments

3 pages

R2 v1 2026-07-22T17:37:05.576Z