Stability of semigroups commuting with a compact operator

Radicals Commuting with Bands of Semigroups

It is known that ring and semigroup theories have evolved many similar methods. The exchange of ideas between these theories has enriched both of them. Among ring concepts transfered to semigroups, the notion of a radical deserves mentioning. The analogy with radicals of rings suggests that semigroup radicals may be applicable in studying the structure of semigroups. On the other hand, many str...

Connexion with Operator Semigroups

Commuting semigroups of holomorphic mappings

Let S1 = {Ft}t≥0 and S2 = {Gt}t≥0 be two continuous semigroups of holomorphic self-mappings of the unit disk ∆ = {z : |z| < 1} generated by f and g, respectively. We present conditions on the behavior of f (or g) in a neighborhood of a fixed point of S1 (or S2), under which the commutativity of two elements, say, F1 and G1 of the semigroups implies that the semigroups commute, i.e., Ft◦Gs = Gs◦...

E0-dilation of strongly commuting CP0-semigroups

We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: 1: we show that a strongly commuting pair of CP0semigroups can be represented via a two parameter product system representation; 2: we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation....

Institute for Mathematical Physics Compact Kac Algebras and Commuting Squares Compact Kac Algebras and Commuting Squares Compact Kac Algebras and Commuting Squares Compact Kac Algebras and Commuting Squares

3 We consider commuting squares of nite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to nite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding subfa...