• DOI:10.1007/s00209-019-02255-3
• Corpus ID: 119138614

Completely bounded maps and invariant subspaces

@article{Alaghmandan2017CompletelyBM,
  title={Completely bounded maps and invariant subspaces},
  author={Mahmood Alaghmandan and Ivan G. Todorov and Lyudmila Turowska},
  journal={Mathematische Zeitschrift},
  year={2017},
  volume={294},
  pages={471-489}
}

• M. Alaghmandan, I. Todorov, L. Turowska
• Published 1 September 2017
• Mathematics
• Mathematische Zeitschrift

We provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols. If $$\mathbb {G}$$ G is a locally compact quantum group, we characterise the completely bounded $$L^{\infty }(\mathbb {G})'$$ L ∞ ( G ) ′ -bimodule maps that send $$C_0({\hat{\mathbb {G}}})$$ C 0 ( G ^ ) into $$L^{\infty }({\hat{\mathbb {G}}})$$ L ∞ ( G ^ ) in terms of the properties of the corresponding elements of the normal Haagerup tensor product $$L^{\infty }(\mathbb {G}) \otimes _{\sigma \mathop {\mathrm{h}}} L^{\infty }(\mathbb {G})$$ L ∞ ( G ) ⊗ σ h L ∞ ( G ) . As a consequence, we obtain an intrinsic characterisation of the normal completely bounded $$L^{\infty }(\mathbb {G})'$$ L ∞ ( G ) ′ -bimodule maps that leave $$L^{\infty }({\hat{\mathbb {G}}})$$ L ∞ ( G ^ ) invariant, extending and unifying results, formulated in the current literature separately for the commutative and the co-commutative cases.