NORMS OF VECTOR FUNCTIONALS

作者：Anoussis, M.^*; Ozawa, N.; Todorov, I. G.

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147(5): 2057-2068.

DOI：10.1090/proc/14383

• Vector functional
• von Neumann algebra
• CSL algebra

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.

• 出版日期2019-5
• 单位南开大学