Related papers: Norm and Numerical Peak Holomorphic Functions on B…

For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite…

We study the set $\operatorname{MA}(X,Y)$ of operators between Banach spaces $X$ and $Y$ that attain their minimum norm, and the set $\operatorname{QMA}(X,Y)$ of operators that quasi attain their minimum norm. We characterize the…

We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do…

Let $f$ be a nonzero holomorphic function in the unit ball $\mathbb B$ of the $n$-dimensional complex Euclidean space $\mathbb C^n$ such that the function $f$ vanishes on the set ${\sf Z}\subset \mathbb B$ and satisfies the constraint…

Given $\u$ a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, $H_{b\u}(E)$. We prove that, under very natural conditions verified by many usual classes of…

Let X and Y be complex Banach spaces, B_X be the open unit ball of X and HL(B_X,Y) be the Banach space of all holomorphic Lipschitz maps f:B_X->Y such that f(0)=0, endowed with the Lipschitz norm. Given a Banach operator ideal A, we use the…

We characterize Banach spaces with polynomial numerical index 1 when they have the Radon-Nikod\'ym property. The holomorphic numerical index is introduced and the characterization of the Banach space with holomorphic numerical index 1 is…

We modify the very well known theory of normed spaces $(E, \norm)$ within functional analysis by considering a sequence $(\norm_n : n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$ for each $n\in\N$. Our theory is…

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

In most classical holomorphic function spaces on the unit disk, a function $f$ can be approximated in the norm of the space by its dilates $f\_r(z):=f(rz)~(r \textless{} 1)$. We show that this is \emph{not} the case for the de…

For a real normed space $X$, we study the $n$-dual space of $\left(X,\left\Vert \cdot \right\Vert \right) $ and show that the space is a Banach space. Meanwhile, for a real normed space $X$ of dimension $d\geq n$ which satisfies property…

In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function $f$ can be approximated in norm by its dilates $f_r(z):=f(rz)~(r<1)$, in other words, $\lim_{r\to1^-}\|f_r-f\|=0$. We construct a…

We study the Bishop-Phelps-Bollob\'as property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces ensuring the BPBp-nu. Among other results, we show that $L_1(\mu)$-spaces have this property for every…

We study entropy numbers and box dimension of (the image of) homogeneous polynomials and holomorphic functions between Banach spaces. First, we see that entropy numbers and box dimensions of subsets of Banach spaces are related. We show…

The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms…

A Banach space is said to have the ball-covering property (abbreviated BCP) if its unit sphere can be covered by countably many closed, or equivalently, open balls off the origin. Let $K$ be a locally compact Hausdorff space and $X$ be a…

E. Oja, T. Viil, and D. Werner showed, in [Totally smooth renormings, Archiv der Mathematik, 112, 3, (2019), 269--281] that a weakly compactly generated Banach space $(X,\|\cdot \|)$ with the property that every linear functional on $X$ has…

The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…

For a metric space $X$, we study the space $D^{\infty}(X)$ of bounded functions on $X$ whose infinitesimal Lipschitz constant is uniformly bounded. $D^{\infty}(X)$ is compared with the space $\LIP^{\infty}(X)$ of bounded Lipschitz functions…

We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We…