B. Zalar, Jordan-von Neumann theorem for Saworotnows generalized Hilbert space. Journal of Acta Mathe- matica Hungarica 69, (1995), 301-325.B. Zalar, Jordan-von Neumann theorem for Saworotnow's generalized Hilbert space, Acta Math. Hungar., 69 (1995), 301-325....
type I_2 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...
Kadison showed that several partial structures of M can recover the von Neumann algebra up to Jordan ⁎-isomorphisms. In particular, each of the following is a complete Jordan ⁎-invariant of M: the Banach space structure of the self-adjoint part Msa of M ([4, Theorem 2]), the ...
It is shown that the category of homogeneous self-dual cones in Hilbert spaces is isomorphic to the category of Jordan Banach algebras with predual (JBW-algebras).
vonNeumann algebrascontext,motivatedbythe theory ofquantum dynamical systems.Fromthe physicalpointofviewthemostimportantarethestudy oftheaveragesofcontinuousorpositivemapsonC- orW一algebrasbutinthecontextofthispaperitseems t0bealsonaturaltoconsidertheergodicbehaviorof ...
The corresponding representation theorem can be considered as a generalization of (the original form of) the classical Jordan–von Neumann characterization of complex inner product spaces.doi:10.1007/s10474-011-0075-5Dijana IlieviSpringer NetherlandsActa Mathematica Hungarica...
For finite-dimensional normed vector spaces over , we formulate an approximate version of this theorem: if a space approximately satisfies the parallelogram law, then it has a near isometry with Euclidean space. In other words, a small von Neumann Jordan constant for yields a small Banach–Mazur...
The quadratic case is the "parallelogram law" which distinguishes Hilbert spaces among Banach spaces.doi:10.1016/0001-8708(73)90111-4David LubellElsevier Inc.Advances in Mathematics
Park C, Cho Y, Han M: Functional inequalities associated with Jordan-von Neumann type additive functional equations. J. Inequal. Appl. 2007., 2007: Article ID 41820C. Park, Y. Cho and M. Han, Functional inequalities associated with Jordan-von Neumann type additive functional equations, J. ...
von Neumann algebrasalgebrastriples46L5146L1046L3017C65We establish Lyapunov type theorems on automatic convexity of various affine transformations of the set of extreme points of important convex sets (closed unit ball, positive part of the closed unit ball, state space) appearing in the theory ...