On a problem of Kadison and Singer.
On an application of a Newton-like method to the approximation of implicit functions
On Banach ideals determined by Banach lattices and their applications [Book]
On quasi-compactness of operator nets on Banach spaces
The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net is equivalent to quasi-compactness of some operator . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.
On reflexivity of representations of local Commutative Algebras
On some Banach ideals of operators
On some classes of linear function transformations of sequences (III)
On some consequences of a generalized continuity
In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "" with arbitrary linear regular summability methods we consider the notion of a generalized continuity (-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.
On the compact approximation property
We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net of compact operators on X such that and in the strong operator topology. Similar results for dual spaces are also proved.
On the differentiability of the norm in trace classes
On the dual of L(E, F).
On the geometry of spaces of K-valued operators
On the Metric Geometry of Ideals of Operators on Hubert Space.
On the norm of a projection onto the space of compact operators
Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than max|B| + c....
On the reflexivity and hyperreflexivity of algebras and subspaces
A review of recent reflexivity and hyperreflexivity results is presented. We concentrate particularly on a finite-dimensional situation, Toeplitz operators and partial isometries. Open problems in this area are given.
On the reflexivity of multigenerator algebras [Book]
On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane
The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between spaces on the unit circle and the real line...
On the surjective (injective) envelope of strictly (co-) singular operators
On the uncomplemented subspace
On weakly compact operators.