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Search: MSC category 47L80
( Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) )
1. CMB 2013 (vol 57 pp. 270)
 Didas, Michael; Eschmeier, Jörg

Derivations on Toeplitz Algebras
Let $H^2(\Omega)$ be the Hardy space on a strictly pseudoconvex domain $\Omega \subset
\mathbb{C}^n$,
and let $A \subset L^\infty(\partial \Omega)$ denote the subalgebra of all $L^\infty$functions $f$
with compact Hankel operator $H_f$. Given any closed subalgebra $B \subset A$ containing $C(\partial \Omega)$,
we describe the first Hochschild cohomology group of the
corresponding Toeplitz algebra $\mathcal(B) \subset B(H^2(\Omega))$.
In particular, we show that every derivation on $\mathcal{T}(A)$ is inner. These results are new even for $n=1$,
where it follows that every derivation on $\mathcal{T}(H^\infty+C)$ is inner, while there are noninner
derivations on $\mathcal{T}(H^\infty+C(\partial \mathbb{B}_n))$ over
the unit ball $\mathbb{B}_n$ in dimension $n\gt 1$.
Keywords:derivations, Toeplitz algebras, strictly pseudoconvex domains Categories:47B47, 47B35, 47L80 

2. CMB 2005 (vol 48 pp. 251)
 Murphy, G. J.

The Index Theory Associated to a NonFinite Trace on a $C^\ast$Algebra
The index theory considered in this paper, a
generalisation of the classical Fredholm index theory, is obtained
in terms of a nonfinite trace on a unital $C^\ast$algebra. We relate
it to the index theory of M.~Breuer, which is developed in a
von~Neumann algebra setting, by means of a representation theorem.
We show how our new index theory can be used to obtain an index
theorem for Toeplitz operators on the compact group $\mathbf{U}(2)$,
where the classical index theory does not give any interesting result.
Categories:46L, 47B35, 47L80 
