Norms of vector functionals
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- by M. Anoussis, N. Ozawa and I. G. Todorov PDF
- Proc. Amer. Math. Soc. 147 (2019), 2057-2068 Request permission
Abstract:
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.References
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Additional Information
- M. Anoussis
- Affiliation: Department of Mathematics, University of the Aegean, 83200 Samos, Greece
- Email: mano@aegean.gr
- N. Ozawa
- Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
- Email: narutaka@kurims.kyoto-u.ac.jp
- I. G. Todorov
- Affiliation: Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast BT7 1NN, United Kingdom; and School of Mathematical Sciences, Nankai University, 94 Weijin Road, Tianjin, 300071, People’s Republic of China
- MR Author ID: 693462
- Email: i.todorov@qub.ac.uk
- Received by editor(s): March 28, 2018
- Received by editor(s) in revised form: June 20, 2018
- Published electronically: January 28, 2019
- Communicated by: Adrian Ioana
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2057-2068
- MSC (2010): Primary 47L05; Secondary 46L10, 47L35
- DOI: https://doi.org/10.1090/proc/14383
- MathSciNet review: 3937682