On almost complex structures on abstract Wiener spaces
type: Item
instance of: scholarly article
title: On almost complex structures on abstract Wiener spaces
zbMATH Open document ID: 0852.60064
author: Setsuo Taniguchi
published in: Osaka Journal of Mathematics
publication date: 1996-12-02T00:00:00Z
review text: Let \((B, H, \mu)\) be a real abstract Wiener space; \(B\) is a real separable Banach space, \(H\) is a real separable Banach space imbedded in \(B\) continuously and densely, and \(\mu\) is a Gaussian measure on \(B\). From a geometrical point of view based on the Malliavin calculus, the space \(H\) is thought of as a tangent space of \(H\). An isometry \(J : H \to H\) is said to be an almost complex structure if \(J^2 = -\text{Id}_H\), following the notion on finite-dimensional manifolds. A Newlander-Nirenberg type theorem on the almost complex structure on \(B\) is established; \(J\) admits a natural complex abstract Wiener space \((B_J, H_J, \mu_J)\) and \(B_J\) can be identified with \(B\) in a measure theoretical sense or an exact sense under a suitable condition on \(J\) as a mapping of \(B\) to \(B\). A set function which can distinguish if a point is in \(H\) or not is also introduced on an abstract Wiener space with a nice almost complex structure, and an Egorov theorem is shown with respect to the set function.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 902861
zbMATH Keywords: abstract Wiener space
zbMATH Keywords: Gaussian measure
zbMATH Keywords: Malliavin calculus
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 902861