Nest space decomposition for an operator in βω
New examples of weakly compact approximation in Banach spaces.
Noncommutative function theory and unique extensions
We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő -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 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...
Noncommutative uniform algebras
We show that a real Banach algebra A such that ||a²|| = ||a||² for a ∈ A is a subalgebra of the algebra of continuous quaternion-valued functions on a compact set X.
Non-hyperreflexive reflexive spaces of operators
We study operators whose commutant is reflexive but not hyperreflexive. We construct a C₀ contraction and a Jordan block operator associated with a Blaschke product B which have the above mentioned property. A sufficient condition for hyperreflexivity of is given. Some other results related to hyperreflexivity of spaces of operators that could be interesting in themselves are proved.
Non-Leibniz algebras
Nonlinear maps preserving Lie products on triangular algebras
In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.
Non-reflexive pentagon subspace lattices
Norm attaining operators
Nuclear JC-algebras and tensor products of types.