Related papers: A dual method of constructing hereditarily indecom…

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…

This paper deals with the following types of problems: Assume a Banach space $X$ has some property (P). Can it be embedded into some Banach space $Z$ with a finite dimensional decomposition having property (P), or more generally, having a…

Motivated by the construction of the free Banach lattice generated by a Banach space, we introduce and study several vector and Banach lattices of positively homogeneous functions defined on the dual of a Banach space $E$. The relations…

We show that if $X$ is a sequentially reflexive Banach space, then its Mackey dual $(X^{*},\tau (X^{*}, X))$ is an angelic space. This builds on a result of J. Howard which says that in the Mackey dual $(X^{*}, \tau (X^{*}, X))$ of a Banach…

We address the following question: what is the class of Banach spaces isomorphic to subspaces of indecomposable Banach spaces? We show that this class includes all Banach spaces of density not bigger than the continuum which do not admit…

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…

A. Szankowski's example is used to construct a Banach space similar to that of "An example of an asymptotically Hilbertian space which fails the approximation property", P.G. Casazza, C.L. Garc\'{\i}a, W.B. Johnson [math.FA/0006134…

In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…

Some special Hilbert spaces are introduced to present the class of infinitesimal operators with complete minimal non-basis family of eigenvectors. The discrete Hardy inequality plays an important role in the proposed approach. The…

In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant…

An example of an infinite dimensional and separable Banach space is given, that is not isomorphic to a subspace of l1 with no infinite equilateral sets.

We construct a compact linearly ordered space $K$ of weight aleph one, such that the space $C(K)$ is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, $K$ is a continuous image of a…

In this article, we prove the existence of a non-trivial hyperinvariant subspace for a subclass of compact perturbations of scalar multiple of a partial isometry. Later, we illustrate that this class contains several important classes of…

We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the…

Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a…

In this article, we introduce the concept of weakly uniquely stationary representations. This framework enables us to investigate the complementability of closed subspaces within the context of continuous cohomology with coeffcients in…

Several new characterizations of the Gelfand-Phillips property are given. We define a strong version of the Gelfand-Phillips property and prove that a Banach space has this stronger property iff it embeds into $c_0$. For an infinite compact…

In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\u{\i} space $\mathcal G$ (the…

A Banach space $X$ is said to have the Daugavet property if every operator $T: X\to X$ of rank~$1$ satisfies $\|Id+T\| = 1+\|T\|$. We show that then every weakly compact operator satisfies this equation as well and that $X$ contains a copy…

Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace…