Completely bounded maps and invariant subspaces

Mahmood Alaghmandan, Ivan Todorov, Lyudmila Turowska

Research output: Contribution to journalArticle

Abstract

We provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols. If G is a locally compact quantum group, we characterise the completely bounded L ∞(G) 0 -bimodule maps that send C0(Gˆ ) into L ∞(Gˆ ) in terms of the properties of the corresponding elements of the normal Haagerup tensor product L ∞(G) ⊗σ h L ∞(G). As a consequence, we obtain an intrinsic characterisation of the normal completely bounded L ∞(G) 0 -bimodule maps that leave L ∞(Gˆ ) invariant, extending and unifying results, formulated in the current literature separately for the commutative and the co-commutative cases.
Original languageEnglish
Number of pages19
JournalMathematische Zeitschrift
Early online date12 Feb 2019
DOIs
Publication statusEarly online date - 12 Feb 2019

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Completely Bounded Maps
Bimodule
Invariant Subspace
Compact Quantum Group
Locally Compact
Tensor Product
Invariance
Invariant

Cite this

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Completely bounded maps and invariant subspaces. / Alaghmandan, Mahmood; Todorov, Ivan; Turowska, Lyudmila.

In: Mathematische Zeitschrift, 12.02.2019.

Research output: Contribution to journalArticle

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T1 - Completely bounded maps and invariant subspaces

AU - Alaghmandan, Mahmood

AU - Todorov, Ivan

AU - Turowska, Lyudmila

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AB - We provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols. If G is a locally compact quantum group, we characterise the completely bounded L ∞(G) 0 -bimodule maps that send C0(Gˆ ) into L ∞(Gˆ ) in terms of the properties of the corresponding elements of the normal Haagerup tensor product L ∞(G) ⊗σ h L ∞(G). As a consequence, we obtain an intrinsic characterisation of the normal completely bounded L ∞(G) 0 -bimodule maps that leave L ∞(Gˆ ) invariant, extending and unifying results, formulated in the current literature separately for the commutative and the co-commutative cases.

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