Linear operators which commute with translations. Part I: Representation theorems
نویسندگان
چکیده
منابع مشابه
Commutators Which Commute with One Factor
Let A and B be n × n matrices, let C = ABA−1B−1 be the multiplicative commutator of A and B, and assume AC = CA. Olga Taussky (1961) examined the structure of A and B for the case where A and B are unitary. Marcus and Thompson (1966) generalized her results to the case where A and C are assumed normal. We look at this problem for general A, with particular attention to the cases where A is diag...
متن کاملSaturation theorems for diseretized linear operators
There is a well developed theory of saturation for positive convolution operators on C*, the space of 2n-periodic and continuous functions. Up until recently, this was suitable to handle almost all the important approximation processes on C*. Now, however, some new and interesting sequences of operators have been obtained for C* by discretizing convolution operators [1], [5]. Such a discretized...
متن کاملThe Representation of Linear Operators
A satisfactory representation theory in terms of integrals for linear operators from an Lp space to an arbitrary Banach space X has not as yet been developed for p>l. For the case p = l, Dunford and Pettis [3] have obtained results provided X satisfies certain rather general restrictions. In particular, the representations for the cases in which X is an L space or an Lp space are well known. Th...
متن کاملTheory of Operators Part I. Single Operators
The work of von Neumann on Operator Theory as distinct from the later work on Rings of operators, extends from 1928 to 1932 with certain later additions. I t is a remarkable development in which the inadequacy of formula mathematics for quantum mechanics was established and a new abstract approach introduced. This approach required the abstract definition of Hubert space and reformulation of th...
متن کاملPolynomial Extension Operators. Part I
In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1966
ISSN: 0004-9735
DOI: 10.1017/s1446788700004286