The Nielsen product formula for coincidences

The Three Faces of Nielsen: Coincidences, Intersections and Preimages

In addition to the many diierent Nielsen-type numbers that have been introduced to study xed points, there are Nielsen-type numbers that have been created to study coincidences of maps; intersections of maps; and preimages of maps. These problems, while distinct, are all similar, and the Nielsen theories that have been created to study them display strong structural similarities as well. In thi...

Estimating Nielsen Numbers on Wedge Product Spaces

Trotter's product formula for projections

where the limit is taken in the strong operator topology (see e.g. Goldstein [G, Theorem 8.12.] or ChernofF [C] for a comprehensive treatment of product formulas). Now let P G £ (E) be a contractive projection. Then we may consider P as a constant degenerate semigroup on E. It is interesting to know under which circumstances the limit in (1) exists if we replace e by P. More precisely, we ask f...

A Formula for the Direct Product of Crossed Product Algebras

tive radius r. Let the center Xo be the sequence {&?}, and let 5 be chosen so large that 2~~ + 2~ s 2 + • • • k Q s. If we define xi as (ki, &2> ' * • » $j j8+i, is+2, • • • ), then xi belongs to K and limn fn(xi) = + °°Consequently xi cannot be a point of Up and this contradiction establishes U as a set of the f...

Trotter’s product formula for projections

The aim of this paper is to examine the convergence of Trotter’s product formula when one of the C0-semigroups is replaced by a projection (which can always be regarded as a constant degenerate semigroup). The motivation to study Trotter’s formula in this setting arises from the fact that for ’nice’ open sets Ω ∈ R the C0-semigroup on L(Ω) generated by the Laplacian with Dirichlet boundary cond...