2011
DOI: 10.1090/s0002-9939-2010-10673-1
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Characterization of subdiagonal algebras

Abstract: Abstract. Let M be a finite von Neumann algebra with a faithful normal tracial state τ, and let A be a tracial subalgebra of M. We show that A has L p -factorization (1 ≤ p < ∞) if and only if A is a subdiagonal algebra. Also, we obtain some characterizations of subdiagonal algebras. IntroductionLet M be a finite von Neumann algebra with a faithful normal tracial state τ. In [1], Arveson introduced the notion of finite, maximal, subdiagonal algebras A of M, as noncommutative analogues of weak-* Dirichlet algeb… Show more

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Cited by 4 publications
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“…In [4] and [5], among other things, Blecher and Labuschagne proved that a tracial subalgebra [4,Definition 5.5] A has an L ∞ -factorization if and only if A is a subdiagonal algebra. In [3] it was shown that if a tracial subalgebra has an L p -factorization (0 < p < ∞), then it is a subdiagonal algebra.…”
Section: Introductionmentioning
confidence: 99%
“…In [4] and [5], among other things, Blecher and Labuschagne proved that a tracial subalgebra [4,Definition 5.5] A has an L ∞ -factorization if and only if A is a subdiagonal algebra. In [3] it was shown that if a tracial subalgebra has an L p -factorization (0 < p < ∞), then it is a subdiagonal algebra.…”
Section: Introductionmentioning
confidence: 99%