Related papers: Maximal subspaces of strong continuity for composi…

An interesting result by T. Kato and A. Pazy says that a contractive semigroup (T(t)) on a uniformly convex space X is holomorphic iff limsup_{t \downarrow 0} ||T(t)-Id|| < 2. We study extensions of this result which are valid on arbitrary…

The first part of this article is a brief survey of the properties of so-called almost interior points in ordered Banach spaces. Those vectors can be seen as a generalization of ``functions which are strictly positive almost everywhere'' on…

We consider a semigroup of operators in the Banach space $C_b(H)$ of uniformly continuous and bounded functions on a separable Hilbert space $H$. In particular, we deal with semigroups that are related to solution of stochastic PDEs in $H$…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

We prove that if $\{\phi_t\}_{t \geq 0}$ is a CP-semigroup acting on a von Neumann algebra $M \subseteq B(H)$, then for every $A\in M$ and $\xi \in H$, the map $t \mapsto \phi_t(A)\xi$ is norm-continuous. We discuss the implications of this…

The main purpose of this paper is to treat semigroups properties, like norm continuity, compactness and differentiability for perturbed semigroups in Banach spaces. In particular, we investigate three large classes of perturbations,…

We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in $\mathbb{C}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness…

Given a Banach space we consider the $\sigma$-ideal of all of its subsets which are covered by countably many hyperplanes and investigate its standard cardinal characteristics as the additivity, the covering number, the uniformity, the…

We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces,…

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal…

We study some fundamental properties of semicocycles over semigroups of self-mappings of a domain in a Banach space. We prove that any semicocycle over a jointly continuous semigroup is itself jointly continuous. For semicocycles over…

We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…

Let $\A$ be the operator which assigns to each $m \times n$ matrix-valued function on the unit circle with entries in $H^\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \times n$ matrix-valued functions…

We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X=N of natural numbers containing a given subsemigroup W of T(X) where each element of a given set $U$ is a generator of T(X) modulo W. This note…

Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to…

We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…

Using the variational method, it is shown that the set of all strong peak functions in a closed algebra $A$ of $C_b(K)$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we can induce the…

We give a self-contained and introductory account of some basic functional analytic tools needed to understand maximal monotone operators in Hilbert spaces. We review domains of (possibly unbounded) operators, closed sets and closed…

Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite dimensional Fr\'echet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit…