Spectral theory for semi-groups of linear operators

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...

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...

Semi-groups of Operators

Is There a Spectral Theory for All Bounded Linear Operators?

What Is Spectral Theory? By spectral theory we mean the theory of structure of certain bounded linear operators on a Hilbert space. In a broader sense, the history of spectral theory goes way back to the nineteenth century, when the objects of study used to be infinite systems of linear equations and integral equations. The subject was revolutionized in the late 1920s by von Neumann, when he de...

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...