Related papers: Operator Ideals arising from Generating Sequences

We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…

In this paper we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same…

We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

We study almost L(M) weakly compact and order L(M) weakly compact operators in Banach spaces. Several further topics related to these operators are investigated.

We construct an infinite dimensional Banach space of continuous functions C(K) such that every one-to-one operator on C(K) is onto.

Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on…

For an arbitrary operator A on a Banach space X which is a generator of C_0-group with certain growth condition at the infinity, the direct theorems on connection between the smoothness degree of a vector $x\in X$ with respect to the…

We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples…

Let $A$ be a Banach algebra. For $f\in A^{\ast}$, we inspect the weak sequential properties of the well-known map $T_f:A\to A^{\ast}$, $T_f(a) = fa$, where $fa\in A^{\ast}$ is defined by $fa(x) = f(ax)$ for all $x\in A$. We provide…

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…

In this note, we consider the smallest submaximal space structure {\mu}(X) on a Banach space X. We derive a characterization of {\mu}(X) up to complete isometric isomorphism in terms of a universal property. Also, we show that an injective…

It is well known that iterates of quasi-compact operators converge towards a spectral projection, whereas the explicit construction of the limiting operator is in general hard to obtain. Here, we show a simple method to explicitly construct…

We formulate general conditions which imply that $L(X,Y)$, the space of operators from a Banach space $X$ to a Banach space $Y$, has $2^{\mathfrak c}$ closed ideals where $\mathfrak c$ is the cardinality of the continuum. These results are…

In this paper, we investigate more about relationship between $uaw$ -convergence (resp. $un$-convergence) and the weak convergence. More precisely, we characterize Banach lattices on which every weak null sequence is $uaw$-null. Also, we…

For $C^*$-algebras $A$ and $B$, we prove the slice map conjecture for ideals in the operator space projective tensor product $A \hat\otimes B$. As an application, a characterization of prime ideals in the Banach $\ast$-algebra $A\hat\otimes…

In this paper we introduce and study a new class of operators related to norm bounded sets on Banach Lattice and which brings together several classical classes of operators (as o-weakly compact operators, b-weakly compact operators,…

We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This…

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce two types of continuous operators between Banach lattices using unbounded absolute weak convergence. We…

The question which led to the title of this note is the following: {\it If $X$ is a Banach space and $K$ is a compact subset of $X$, is it possible to find a compact, or even approximable, operator $v:X\to X$ such that…