Related papers: Constructions of sequential spaces

We investigate uniform, strong, weak and almost weak stability of multiplication semigroups on Banach space valued $L^p$-spaces. We show that, under certain conditions, these properties can be characterized by analogous ones of the…

The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also…

We introduce a new norm, called $N^{p}$-norm $(1\leq{p}<\infty)$ on a space $N^{p}(V,W)$ where $V$ and $W$ are abstract operator spaces. By proving some fundamental properties of the space $N^{p}(V,W)$, we also obtain that if $W$ is…

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces

In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…

For $1\le p <\infty$, we present a reflexive Banach space $\mathfrak{X}^{(p)}_{\text{awi}}$, with an unconditional basis, that admits $\ell_p$ as a unique asymptotic model and does not contain any Asymptotic $\ell_p$ subspaces. D. Freeman,…

The study of the Banach-Saks property in Banach spaces has a long and illustrious history. Of late, motivated by applications in financial mathematics, interest has arisen in the Banach-Saks type properties with respect to order…

We study the double iterated outer $L^p$ spaces, namely the outer $L^p$ spaces associated with three exponents and defined on sets endowed with a measure and two outer measures. We prove that in the case of finite sets, under certain…

We construct a Banach space $\mathcal X_\varepsilon$ with an uncountable $\varepsilon$-biorthogonal system but no uncountable $\tau$-biorthogonal system for $\tau<\varepsilon$. In particular the space have no uncountable biorthogonal…

We prove modulation invariant embedding bounds from Bochner spaces $L^p(\mathbb{W};X)$ on the Walsh group to outer-$L^p$ spaces on the Walsh extended phase plane. The Banach space $X$ is assumed to be UMD and sufficiently close to a Hilbert…

This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order recursion theory and computability in analysis. Among other things it is shown…

We introduce Banach spaces of vector-valued random variables motivated from mathematical finance. So-called risk functionals are defined in a natural way on these Banach spaces and it is shown that these functionals are Lipschitz…

A topological space is said to be sequential if every sequentially closed subspace is closed. We consider Banach spaces with weak*-sequential dual ball. In particular, we show that if $X$ is a Banach space with weak*-sequentially compact…

A Banach space $X$ is said to have property (K) if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly…

We identify simple universal properties that uniquely characterize the Lebesgue $L^p$ spaces. There are two main theorems. The first states that the Banach space $L^p[0, 1]$, equipped with a small amount of extra structure, is initial as…

We discuss $\mathrm{L}^p$ fiber spaces which appear, e.g., as extrapolation spaces of unbounded multiplication operators which in turn are motivated, for instance, by non-autonomous evolution equations.

The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…

We study the behaviour of Whitley's thickness constant of a Banach space with respect to $\ell_p$-products and we compute it for classical $L_p$-spaces.

This article was initially motivated by our goal to show that the Banach space $\mathbb{G}$ constructed by Gowers in [W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), no. 6, 523-530] to settle…

A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or "position") of a Banach space into another and of the relation of isomorphism of complex structures on a real Banach space. The…