Bundle convergence of Cesáro means of orthogonal sequences in noncommutative \(L_2\)-spaces (Q1964601)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Bundle convergence of Cesáro means of orthogonal sequences in noncommutative \(L_2\)-spaces |
scientific article; zbMATH DE number 1404408
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bundle convergence of Cesáro means of orthogonal sequences in noncommutative \(L_2\)-spaces |
scientific article; zbMATH DE number 1404408 |
Statements
Bundle convergence of Cesáro means of orthogonal sequences in noncommutative \(L_2\)-spaces (English)
0 references
21 February 2000
0 references
The author proves a noncommutative counterpart of a theorem by Tandori, Gaposhkin and himself on a sufficient condition for the almost sure convergence of the Cesàro means of order \(\alpha\) of an orthogonal sequence in \(L^2\). The noncommutative \(L^2\) space is the GNS representation space and the almost sure convergence is replaced by the bundle convergence as defined by \textit{E. Hensz, R. Jajte and A. Paszkiewicz} [Stud. Math. 120, No. 1, 23-46 (1996; Zbl 0856.46033)]. The main technical tool is the Sunouchi-Yano identity.
0 references
von Neumann algebra
0 references
faithful and normal state
0 references
preHilbert space
0 references
completion
0 references
Gelfand-Naimark-Segal representation theorem
0 references
bundle convergence
0 references
orthogonal sequence
0 references
Sunouchi-Yano identity
0 references
GNS representation space
0 references
noncommutative \(L^2\) space
0 references
Cesàro means
0 references
