Factorization in Subdiagonal Algebras

✍ Scribed by Guoxing Ji; Kichi-Suke Saito

• Book ID: 102590517
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 250 KB
• Volume: 159
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3309

✦ Synopsis

Let M be a _-finite von Neumann algebra and let A be a maximal subdiagonal algebra of M with respect to a faithful normal conditional expectation 8. We show that if S is an invertible operator in M, then there exists an isometry W in M such that both S &1 W and W*S belong to A. We also give several characterizations of a maximal subdiagonal algebra A such that every invertible operator S in M can be factored as UA, where U is a unitary operator in M and both A and A &1 are in A.