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Noncommutative function theory and unique extensions

David P. BlecherLouis E. Labuschagne — 2007

Studia Mathematica

We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő L p -distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of H from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary...

Outers for noncommutative H p revisited

David P. BlecherLouis E. Labuschagne — 2013

Studia Mathematica

We continue our study of outer elements of the noncommutative H p spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in H p actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ ∈ Ball(A)...

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