An extension of a theorem of Jordan and von Neumann

Stone - von Neumann theorem

The bibliography indicates the origins of these issues in proving uniqueness, up to isomorphism, of the model for the commutation rules of quantum mechanics. As Mackey and Weil observed, some form of the argument succeeds in quite general circumstances. The argument here is an amalgam and adaptation of those in sources in the bibliography. The proof here applies nearly verbatim, with suitable a...

On a Theorem of Von Neumann

1. Introduction. Let 5 be a measure space with a countably additive , (T-finite, complete (non-negative) measure. J. von Neumann has proved that, from each class x of measurable sets modulo null sets of 5, a representative set R(x)Ex can be picked in such a way

On A Theorem of von Neumann.

An Extension of the Weyl-von Neumann Theorem to Normal Operators^)

We prove that a normal operator on a separable Hubert space can be written as a diagonal operator plus a compact operator. If, in addition, the spectrum lies in a rectifiable curve we show that the compact operator can be made HilbertSchmidt. In 1909 Hermann Weyl proved [3] that each bounded Hermitian operator on a separable Hubert space can be written as the sum of a diagonal operator and a co...

The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...