Operator synthesis and tensor products
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- by G. K. Eleftherakis and I. G. Todorov PDF
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Abstract:
We show that Kraus’ property $S_{\sigma }$ is preserved under taking weak* closed sums with masa-bimodules of finite width and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite width. We initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form $\kappa \times \lambda$, where $\kappa$ is a set of finite width while $\lambda$ is operator synthetic, is, under a necessary restriction on the sets $\lambda$, again operator synthetic. We show that property $S_{\sigma }$ is preserved under spatial Morita subordinance.References
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Additional Information
- G. K. Eleftherakis
- Affiliation: Department of Mathematics, Faculty of Sciences, University of Patras, 265 00 Patras, Greece
- Email: gelefth@math.upatras.gr
- I. G. Todorov
- Affiliation: Pure Mathematics Research Centre, Queen’s University Belfast, Belfast BT7 1NN, United Kingdom
- MR Author ID: 693462
- Email: i.todorov@qub.ac.uk
- Received by editor(s): February 5, 2013
- Received by editor(s) in revised form: February 21, 2013, and May 20, 2014
- Published electronically: October 29, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 5271-5300
- MSC (2010): Primary 46A32; Secondary 47L35, 47L05
- DOI: https://doi.org/10.1090/tran/6536
- MathSciNet review: 3458381