A Noncommutative Version of H (p) and Characterizations of Subdiagonal Algebras

作者：Ji, Guoxing^*

来源：Integral Equations and Operator Theory, 2012, 72(1): 131-149.

DOI：10.1007/s00020-011-1920-1

• von Neumann algebra
• subdiagonal algebra
• noncommutative H-p space

Let M be a sigma- finite von Neumann algebra and U a maximal subdiagonal algebra of M with respect to a faithful normal conditional expectation Phi. Based on Haagerup's noncommutative L-p space L-p (M) associated with M, we give a noncommutative version of H-p space relative to U. If h(0) is the image of a faithful normal state phi in L-1 (M) such that phi o Phi = phi, then it is shown that the closure of {Uh(0)(1/p)} in L-p (M) for 1 <= p < infinity is independent of the choice of the state preserving Phi. Moreover, several characterizations for a subalgebra of the von Neumann algebra M to be a maximal subdiagonal algebra are given.

• 出版日期2012-1
• 单位陕西师范大学