Multiple tunnelings in d-dimensions : a quantum particle in a hierarchical potential
Multipliers and hereditary subalgebras of operator algebras
We generalize some technical results of Glicksberg to the realm of general operator algebras and use them to give a characterization of open and closed projections in terms of certain multiplier algebras. This generalizes a theorem of J. Wells characterizing an important class of ideals in uniform algebras. The difficult implication in our main theorem is that if a projection is open in an operator algebra, then the multiplier algebra of the associated hereditary subalgebra arises as the closure...
Multipliers in complex Banach spaces and structure of the unit balls
Nest space decomposition for an operator in βω
New examples of weakly compact approximation in Banach spaces.
(Non-)amenability of ℬ(E)
In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that . Still, ℬ(ℓ²) is not amenable,...
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.
Old and new results on Allan's GB*-algebras
This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication...
On a class of linear operators.
On a functional representation of the lattice of projections on a Hilbert space
On a generalization of W*-modules
a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.
On a problem of Kadison and Singer.
On a result of Peetre about interpolation of operator spaces
We establish interpolation formulæ for operator spaces that are components of a given quasi-normed operator ideal. Sometimes we assume that one of the couples involved is quasi-linearizable, some other times we assume injectivity or surjectivity in the ideal. We also show the necessity of these suppositions.