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}
}
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… 

Reduced spectral synthesis and compact operator synthesis

References

SHOWING 1-10 OF 31 REFERENCES

A REPRESENTATION THEOREM FOR LOCALLY COMPACT QUANTUM GROUPS

Recently, Neufang, Ruan and Spronk proved a completely isometric representation theorem for the measure algebra M(G) and for the completely bounded (Herz–Schur) multiplier algebra McbA(G) on

C*-Algebras and Finite-Dimensional Approximations

Fundamental facts Basic theory: Nuclear and exact $\textrm{C}^*$-algebras: Definitions, basic facts and examples Tensor products Constructions Exact groups and related topics Amenable traces and

Completely isometric representations of $M_{cb}A(G)$ and $UCB(\hat G)^*$

. Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra M cb A ( G ), which is dual to the

Completely bounded bimodule maps and spectral synthesis

We initiate the study of the completely bounded multipliers of the Haagerup tensor product A(G) circle times(h) A(G) of two copies of the Fourier algebra A(G) of a locally compact group G. If E is a

Approximation properties for group *-algebras and group von Neumann algebras

Let G be a locally compact group, let C,' (G) (resp. VN(G)) be the C*-algebra (resp. the von Neumann algebra) associated with the left regular representation I of G, let A(G) be the Fourier algebra

Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras

Let G be a locally compact group, Lp(G) be the usual Lp‐space for 1 ⩽ p ⩽ ∞, and A(G) be the Fourier algebra of G. Our goal is to study, in a new abstract context, the completely bounded multipliers

Completely bounded multipliers over locally compact quantum groups

In this paper, we consider several interesting multiplier algebras associated with a locally compact quantum group G . Firstly, we study the completely bounded right multiplier algebra Mcbr(L1(G)) .

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

For any amenable locally compact group G, the space of multipliers MA(G) of the Fourier algebra A(G) coincides with the space B(G) of functions on G that are linear combinations of continuous

COMPLETELY ISOMETRIC REPRESENTATIONS OF McbA(G) AND UCB(G)

Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra M cb A(G), which is dual to the

Multipliers, Self-Induced and Dual Banach Algebras

In the first part of the paper, we present a short survey of the theory of multipliers, or double centralisers, of Banach algebras and completely contractive Banach algebras. Our approach is very