Lyapunov theorems for operator algebras
著者
書誌事項
Lyapunov theorems for operator algebras
（Memoirs of the American Mathematical Society, no. 458）
American Mathematical Society, 1991
大学図書館所蔵 全21件
注記
"November 1991, volume 94, number 458 (end of volume)" -- T.p
Includes bibliographical references
内容説明・目次
内容説明
In 1940, A A Lyapunov published his celebrated discovery that the range of a nonatomic vector-valued measure is convex and compact. This book presents the result of a systematic generalization of Lyapunov's theorem to the setting of operator algebras. The author's point of view follows that of Lindenstrauss, so that, in their terminology, Lyapunov's theorem asserts that if *v is a weak* continuous map of a nonatomic abelian von Neumann algebra *N into Cn, and B denotes the positive part of the unit ball of *N, then for each a *e B there is an extreme point p of B (i.e., a projection) with *v (p) = *V (a). We begin by studying an affine map *v of a convex subset Q of a linear space X into a linear space y. If *v (E) = *v (Q), where E donotes the extreme points of Q, we say a Lyapunov theorem of type 1 holds. If y is a normed space, we say a Lyapunov theorem of type 2 (resp. type 3) holds if *v (E) is norm dense (resp.*e-dense) in *v (Q). Roughly speaking, a Lyapunov theorem of type 4 asserts that *v maps at least one element of E away from the boundary. Results of all four types are obtained. a face of B, or the entire unit ball of x. If *v is a singular map and is a purely infinite, countably decomposable von Neumann algebra, then the range of *v may be infinite-dimensional.
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