Invariant traces on algebras

Institute for Mathematical Physics Traces on Algebras of Parameter Dependent Pseudodiierential Operators and the Eta{invariant Traces on Algebras of Parameter Dependent Pseudodiierential Operators and the Eta{invariant

We identify Melrose's suspended algebra of pseudodiierential operators with a subalgebra of the algebra of parametric pseudodiierential operators with parameter space R. For a general algebra of parametric pseudodiierential operators, where the parameter space may now be a cone ? R p , we construct a unique \symbol valued trace", which extends the L 2 {trace on operators of small order. This al...

Traces on algebras of parameter dependent pseudodifferential operators and the eta–invariant

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space R. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone Γ ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This c...

Topologically Left Invariant Mean on Dual Semigroup Algebras

Traces on Infinite - Dimensional Brauer Algebras ∗

We describe the central measures for the random walk on graded graphs. Using this description , we obtain the list of all finite traces on three infinite-dimensional algebras: on the Brauer algebra, on the partition algebra, and on the walled Brauer algebra. For the first two algebras, these lists coincide with the list of all finite traces of the infinite symmetric group. For the walled Brauer...

Translation-invariant Function Algebras on Compact Groups

Let X be a compact group. $(X) denotes the Banach algebra (point multiplication, sup norm) of continuous complexvalued functions on X A is any closed subalgebra of d(X) which is stable under right and left translations and contains the constants. It is shown, by means of the Peter-Weyl Theorem and some multilinear algebra, that the condition (*) every representation of degree 1 of X has finite ...