Stochastic integration in finite von Neumann algebras

被引：1

作者：

Luczak, Andrzej ^{[1
]}

Mohammed, Abdulrahman A. A. ^{[1
]}

机构：

[1] Univ Lodz, Fac Math, PL-90131 Lodz, Poland

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2007年 / 44卷 / 02期

关键词：

quantum stochastic integration; quantum stochastic processes; finite von Neumann algebras;

D O I：

10.1556/SScMath.2007.1016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate various aspects of stochastic integration in finite von Neumann algebras. For integration with respect to a bounded L-2-martingale the idea of treating the integral as a bounded operator is developed. Several classes of integrable processes are defined, it turns out that some of them form a Banach or C*-algebra. We find representations of these algebras and establish relations between the von Neumann algebras generated by these representations. Finally, we characterize the range of the stochastic integration operator.

引用

页码：233 / 264

页数：32

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