Operator synthesis and tensor products

2013/01/16 by George Eleftherakis, Ivan G. Todorov, Eleftherakis, G. K. +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1301.3640

openalex publication_date 2013/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Kraus' property S_σ 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 κ× λ, where κ is a set of finite width, while λ is operator synthetic, is, under a necessary restriction on the sets λ, again operator synthetic. We show that property S_σ is preserved under spatial Morita subordinance. En route, we prove that non-atomic ternary masa-bimodules possess property S_σ hereditarily.

Citations

• Morita equivalence of dual operator algebras
• On the Ranges of Bimodule Projections

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• Spectral synthesis and masa-bimodules
• Bilattices and Morita equivalence of masa bimodules
• Weak* tensor products for von Neumann algebras
• Two Generalizations of Tensor Products, Beyond Vector Spaces
• Bisets as categories, and tensor product of induced bimodules