Perturbation Theory 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

Lie Theory of Semi-groups of Linear Transformations

Such families arise in the most varied branches of classical and of modern analysis and are interesting for their own sake as well as for the many applications. An extension to the w-parameter case was presented to the Society in October 1944 (abstract 51-1-15). Here the parameter a = (au ai, • • • , an) is a vector in ^-dimensional real euclidean space En, the operators T(a) are denned for non...

The Perturbation Theory of Some Volterra Operators

A general procedure is derived for obtaining sufficient conditions for the similarity of operators T and T + P. This is applied to obtain sharp conditipns for the similarity of the Volterra operators J: f(x)-+ / f(y)dy and J + P where P: f(x) /+/fp(x,y)f(y)dy. By the same methods perturbations of the one sided shift operator S on LP(Ofo) by certain trace class operators P are shown to be simila...