Details

Autor(en) / Beteiligte

• Paszkiewicz, Adam

Titel

Convergences in W∗-algebras

Ist Teil von

• Journal of functional analysis, 1986, Vol.69 (2), p.143-154

Ort / Verlag

Orlando, FL: Elsevier Inc

Erscheinungsjahr

1986

Link zum Volltext

Quelle

Elsevier Journal Backfiles on ScienceDirect (DFG Nationallizenzen)

Beschreibungen/Notizen

• Let U be a W ∗-algebra with a faithful normal state ϱ; x n in U , n ⩾ 1. Five conditions, each of which generalizes the notion of a.e. convergence for random variables, are studied with the use of some properties of the geometry of projectors from U . The conditions are equivalent if ( x n ) is bounded, and are not equivalent for an arbitrary sequence. Sequences x n → 0 a.u. y n → 0 a.u., x n + y n ↛ 0 a.u. are given. Thus, some problems stated by Batty, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 48 (1979), 177–191, are solved.