On Projection Maps of von Neumann Algebras.
On projectional skeletons in Vašák spaces
We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.
On Projections and monotony in Lp-spaces.
On projections and unconditional bases in direct sums of Banach spaces
On projections and unconditional bases in direct sums of Banach spaces II
On projections in Banach space
On projections in H¹ and BMO
On projections in spaces of bounded analytic functions with applications
On projections of onto translation-invariant subspaces
On projections on subspaces of codimension one
On property in -spaces
On Property β of Rolewicz in Köthe-Bochner Function Spaces
It is proved that the Köthe-Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe-Bochner sequence spaces.
On property (β) of Rolewicz in Köthe-Bochner sequence spaces
We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve...
On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
On pseudonormability of some particular classes of spaces
On p-summable sequences in locally convex spaces.
On Pták’s generalization of Hankel operators
In 1997 Pták defined generalized Hankel operators as follows: Given two contractions and , an operator is said to be a generalized Hankel operator if and satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of and . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat...
On Pták's Generalization of the Open-Mapping and Closed-Graph Theorems.
On Q-independence, limit theorems and q-Gaussian distribution
We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.
On quadratic and sesquilinear functionals.