Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schur and Fourier multipliers of an amenable group acting on
  non-commutative Lp-spaces   Consider a completely bounded Fourier multiplier phi of a locally compact
group G, and take 1 <= p <= infinity. One can associate to phi a Schur
multiplier on the Schatten classes S_p(L^2 G), as well as a Fourier multiplier
on Lp(LG), the non-commutative Lp-space of the group von Neumann algebra of G.
We prove that the completely bounded norm of the Schur multiplier is not
greater than the completely bounded norm of the Lp-Fourier multiplier. When G
is amenable we show that equality holds, extending a result by Neuwirth and
Ricard to non-discrete groups.
  For a discrete group G and in the special case when p > 2 is an even integer,
we show the following. If there exists a map between Lp(LG) and an ultraproduct
of Lp(M) \otimes S_p(L^2 G) that intertwines the Fourier multiplier with the
Schur multiplier, then G must be amenable. This is an obstruction to extend the
Neuwirth-Ricard result to non-amenable groups.

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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg