Completely bounded maps and invariant subspaces

Mahmood Alaghmandan, Ivan Todorov, Lyudmila Turowska

Research output: Contribution to journal › Article

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

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Alaghmandan, Mahmood ; Todorov, Ivan ; Turowska, Lyudmila. / Completely bounded maps and invariant subspaces. In: Mathematische Zeitschrift. 2019.
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Alaghmandan, M, Todorov, I & Turowska, L 2019, 'Completely bounded maps and invariant subspaces', Mathematische Zeitschrift. https://doi.org/10.1007/s00209-019-02255-3

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

In: Mathematische Zeitschrift, 12.02.2019.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Completely bounded maps and invariant subspaces

AU - Alaghmandan, Mahmood

AU - Todorov, Ivan

AU - Turowska, Lyudmila

PY - 2019/2/12

Y1 - 2019/2/12

N2 - 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.

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.

U2 - 10.1007/s00209-019-02255-3

DO - 10.1007/s00209-019-02255-3

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Alaghmandan M, Todorov I, Turowska L. Completely bounded maps and invariant subspaces. Mathematische Zeitschrift. 2019 Feb 12. https://doi.org/10.1007/s00209-019-02255-3

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