Compressible groups

Rok, strany: 2003, 433 - 455

We introduce and initiate a study of a new class of partially ordered abelian groups called compressible groups. The compressible groups generalize the order-unit space of self-adjoint operators on Hilbert space, the directed additive group of self-adjoint elements of a unital $ C^*$@-algebra, lattice-ordered abelian groups with order unit, and interpolation groups with order unit. We identify elements called projections in a compressible group, show that the set $P$ of projections forms an orthomodular poset, and give sufficient conditions, satisfied in a Rickart $ C^*$@-algebra and in an interpolation group with order unit, for $P$ to form an orthomodular lattice.

ISO 690:

Foulis, D. 2003. Compressible groups. In Mathematica Slovaca, vol. 53, no.5, pp. 433-455. 0139-9918.

APA:

Foulis, D. (2003). Compressible groups. Mathematica Slovaca, 53(5), 433-455. 0139-9918.