Completely bounded maps and invariant subspaces

2017/09/01 by Mahmood Alaghmandan, Ivan G. Todorov, Alaghmandan, M. +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1709.00118

openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols. If \mathbbG is a locally compact quantum group, we characterise the completely bounded L^∞(\mathbbG)'-bimodule maps that send C₀(\mathbbG) into L^∞(\mathbbG) in terms of the properties of the corresponding elements of the normal Haagerup tensor product L^∞(\mathbbG) ⊗_σ\rm h L^∞(\mathbbG). As a consequence, we obtain an intrinsic characterisation of the normal completely bounded L^∞(\mathbbG)'-bimodule maps that leave L^∞(\mathbbG) invariant, extending and unifying results, formulated in the current literature separately for the commutative and the co-commutative cases.

Citations

• Multipliers of the Fourier Algebras of Some Simple Lie Groups and Their Discrete Subgroups

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