Completely bounded bimodule maps and spectral synthesis
Artikel i vetenskaplig tidskrift, 2017

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 closed subset of G we let E# = {(s, t) : st. E} and show that if E# is a set of spectral synthesis for A(G) circle times(h) A(G) then E is a set of local spectral synthesis for A(G). Conversely, we prove that if E is a set of spectral synthesis for A(G) and G is a Moore group then E# is a set of spectral synthesis for A(G)circle times(h) A(G). Using the natural identification of the space of all completely bounded weak* continuous VN(G)' bimodule maps with the dual of A(G)circle times(h) A(G), we show that, in the case G is weakly amenable, such a map leaves the multiplication algebra of L-infinity(G) invariant if and only if its support is contained in the antidiagonal of G.

Fourier algebra

completely bounded map

bimodule

operator space

Författare

Mahmood Alaghmandan

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

I. G. Todorov

Queen's University Belfast

Lyudmyla Turowska

Chalmers, Matematiska vetenskaper

Göteborgs universitet

International Journal of Mathematics

0129-167X (ISSN)

Vol. 28 10 1750067

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1142/S0129167X17500677