### Abstract

Original language | English |
---|---|

Pages (from-to) | 2057-2068 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 5 |

DOIs | |

Publication status | Published - 28 Jan 2019 |

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### Cite this

*Proceedings of the American Mathematical Society*,

*147*(5), 2057-2068. https://doi.org/10.1090/proc/14383

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*Proceedings of the American Mathematical Society*, vol. 147, no. 5, pp. 2057-2068. https://doi.org/10.1090/proc/14383

**Norms of Vector Functionals.** / Anoussis, M.; Ozawa, N.; Todorov, I. G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Norms of Vector Functionals

AU - Anoussis, M.

AU - Ozawa, N.

AU - Todorov, I. G.

PY - 2019/1/28

Y1 - 2019/1/28

N2 - We examine the questions of when and how the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. We introduce a related operator algebraic property and show that it is satisfied by all von Neumann algebras and by all CSL algebras. We exhibit examples of operator algebras that do not satisfy the property or any scaled version of it.

AB - We examine the questions of when and how the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. We introduce a related operator algebraic property and show that it is satisfied by all von Neumann algebras and by all CSL algebras. We exhibit examples of operator algebras that do not satisfy the property or any scaled version of it.

U2 - 10.1090/proc/14383

DO - 10.1090/proc/14383

M3 - Article

VL - 147

SP - 2057

EP - 2068

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -