Generalised Jordan-von Neumann constants and uniform normal structure

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...

Abelian Subalgebras and the Jordan Structure of a Von Neumann Algebra

For von Neumann algebras M,N not isomorphic to C C and without type I2 summands, we show that for an order-isomorphism f : AbSub M! AbSub N between the posets of abelian von Neumann subalgebras of M and N , there is a unique Jordan ⇤-isomorphism g : M! N with the image g[S] equal to f(S) for each abelian von Neumann subalgebra S of M. The converse also holds. This shows the Jordan structure of ...

Jordan-von Neumann Constant for Banaś-fra̧czek Space

For any λ ≥ 1, Rλ is Banaś-Fra̧czek space, the exact value of the Jordan–von Neumann constant CNJ(Rλ) is investigated. By careful calculations, CNJ(Rλ) = 2− 1 λ2 is given.

Representation of faithful normal expectations in von Neumann algebras

Unitary Orbits of Normal Operators in Von Neumann Algebras

The starting points for this paper are simple descriptions of the norm and strong* closures of the unitary orbit of a normal operator in a von Neumann algebra. The statements are in terms of spectral data and do not depend on the type or cardinality of the algebra. We relate this to several known results and derive some consequences, of which we list a few here. Exactly when the ambient von Neu...