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1. CMB 2012 (vol 57 pp. 166)
On Minimal and Maximal $p$-operator Space Structures We show that for $p$-operator spaces, there are natural notions of minimal and maximal
structures. These are useful for dealing with tensor products.
Keywords:$p$-operator space, min space, max space Categories:46L07, 47L25, 46G10 |
2. CMB 2011 (vol 54 pp. 654)
Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm |
Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely
bounded multipliers of $A(G)$, and let $A_{\mathit{Mcb}}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We
characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \subset G$ is a norm
one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we
describe the closed ideals of $A_{\mathit{Mcb}}(G)$ with an approximate identity bounded by $1$, and we characterize
those $G$ for which $A_{\mathit{Mcb}}(G)$ is $1$-amenable in the sense of B. E. Johnson. (We can even slightly
relax the norm bounds.)
Keywords:amenability, bounded approximate identity, $cb$-multiplier norm, Fourier algebra, norm one idempotent Categories:43A22, 20E05, 43A30, 46J10, 46J40, 46L07, 47L25 |
3. CMB 2005 (vol 48 pp. 97)
On the Ranges of Bimodule Projections We develop a symbol calculus for normal bimodule maps over a masa
that is the natural analogue of the Schur product theory. Using
this calculus we are easily able to give a complete description of
the ranges of contractive normal bimodule idempotents that avoids
the theory of J*-algebras.
We prove that if $P$ is a normal
bimodule idempotent and $\|P\| < 2/\sqrt{3}$ then $P$ is a
contraction. We finish with some attempts at extending the symbol
calculus to non-normal maps.
Categories:46L15, 47L25 |
4. CMB 2003 (vol 46 pp. 632)
The Operator Amenability of Uniform Algebras We prove a quantized version of a theorem by M.~V.~She\u{\i}nberg:
A uniform algebra equipped with its canonical, {\it i.e.}, minimal,
operator space structure is operator amenable if and only if it is
a commutative $C^\ast$-algebra.
Keywords:uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space Categories:46H20, 46H25, 46J10, 46J40, 47L25 |