Related papers: Quotients of Banach spaces with the Daugavet prope…

We study the presence of $L$-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that, if $\dens(Y)\leq \omega_1$ and $G:X\longrightarrow Y$ is a Daugavet center, then $G(W)$ contains some $L$-orthogonal…

We show that the predual of a JBW$^*$-triple has the weak Banach-Saks property, that is, reflexive subspaces of a JBW$^*$-triple predual are super-reflexive. We also prove that JBW$^*$-triple preduals satisfy the Koml\'os property (which…

We characterise the weak$^*$ symmetric strong diameter $2$ property in Lipschitz function spaces by a property of its predual, the Lipschitz-free space. We call this new property decomposable octahedrality and study its duality with the…

It is shown that if the dual of a Banach space, $X^*$, where the dual ball is weak* sequentially compact, has the weak* uniform Kadec-Klee property then $X^*$ has Property($K^*$). An example is given where the reverse implication does not…

In this thesis we explore the the possibility of characterising C* algebras by their (non-isometric) Banach algebra structure alone. We introduce a property of Banach algebras, the Total Reduction Property, and conjecture that a Banach…

We discuss a set-valued generalization of strong proximinality in Banach spaces, introduced by J. Mach [Continuity properties of Chebyshev centers, J. Approx. Theory, 29(3):223--230, 1980] as property-$(P_1)$. We establish that if the…

We investigate the interplay among three key properties of bounded linear operators between Banach spaces: the Bhatia-\v{S}emrl property, strong subdifferentiability and the condition that the essential norm is strictly less than the…

We provide a Laakso construction to prove that the property of having an equivalent norm with the property $(\beta)$ of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between separable Banach spaces. On the…

We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on…

We show that on the unit ball of a certain separable Banach space there is a smooth delbar-closed (0,1)-form which is not locally delbar-exact. Further, the Dolbeault isomorphism theorem does not generalize to arbitrary Banach spaces.…

In this paper, we first study some elementary properties of a typical positive contraction on $\ell_q$ for the Strong Operator Topology and the Strong* Operator Topology. Using these properties, we prove that a typical positive contraction…

We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13].

We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting…

We study structural properties of Wiener-Lebesgue spaces with respect to a slowly varying metrics and certain Lebesgue parameters. For $p\in (0,1]$, we deduce Schatten-$p$ properties for pseudo-differential operators whose symbols, together…

A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the…

For a compact space $K$, the Banach space $C(K)$ is said to have the $\ell_1$-Grothendieck property if every weak* convergent sequence $\big\langle\mu_n\colon\ n\in\omega\big\rangle$ of functionals on $C(K)$ such that $\mu_n\in\ell_1(K)$…

It is shown that if $1<p<\infty$ and $X$ is a subspace or a quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces, then for any compact operator $T$ on $X$ such that $\|I+T\|>1$, the operator $I+T$ attains its norm. A…

This paper studies a dyadic version of fractional Sobolev spaces in $\mathbb{R}^n$ for $n\geq 1$. It provides new proofs of the corresponding fractional Sobolev embedding as well as the algebra property of the spaces, which rely solely on…

Some necessary and sufficient conditions are found for Banach function lattices to have the Radon-Nikod\'ym property. Consequently it is shown that an Orlicz space $L_\varphi$ over a non-atomic $\sigma$-finite measure space $(\Omega,…

A Banach space $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable (QHI) property if $X/Y$ is hereditarily indecomposable (HI) for any infinite codimensional subspace $Y$ with a successive…