A perturbation theorem for semi-groups of linear operators

A Note on Perturbation Theory for Semi-groups of Operators

1. I. S. Cohen, Commutative rings with restricted minimum conditions, Duke Math. J. 17 (1950), 27-41. 2. S. MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771-782. 3. N. Nakano, Idealtheorie in einem speziellen unendlichen algebraischen Zahlkorper, J. Sei. Hiroshima Univ. 16(1953), 425-439. 4. O. Zariski and P. Samuel, Commutative a...

On Fixed Points for Semi-groups of Linear Operators

That such theorems, when applied to the space X of bounded functions on a set S, have measure-theoretic significance was noted in [3]. Let 77 be a semi-group of 1-1 transformations of S into S. To each a EH we correspond the transformation T, of X into itself where T„(f) is the function f(a(s)), sES,fEX. These transformations form a semi-group G each element of which has norm one. Furthermore G...

Semi-groups of Operators

A splitting theorem for linear polycyclic groups

We prove that an arbitrary polycyclic by finite subgroup of GL(n,Q) is up to conjugation virtually contained in a direct product of a triangular arithmetic group and a finitely generated diagonal group.

A purity theorem for linear algebraic groups

Given a characteristic zero field k and a dominant morphism of affine algebraic k-groups μ : G → C one can form a functor from k-algebras to abelian groups R 7→ F(R) := C(R)/μ(G(R)). Assuming that C is commutative we prove that this functor satisfies a purity theorem for any regular local k-algebra. Few examples are considered in the very end of the preprint.