We introduce extensions of $\Delta$-points and Daugavet points in which slices are replaced by relatively weakly open subsets (super super points) or convex combinations (ccs ccs p

Abstract In this paper we analyse when every element of $$X{\widehat{\otimes }}_\pi Y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>X</mml:mi> <mml:msub> <mml:mover> <mml:mo>⊗</mml:mo> <mml:mo>^</mml:mo> </mml:mover> <mml:mi>π</mml:mi> </mml:msub> <mml:mi>Y</mml:mi> </mml:mrow> </mml:math> attains its projective norm. We prove that is the case if X dual a subspace predual an $$\ell _1(I)$$ <mml:mi>ℓ</mml:mi> <mml:mn>1</mml:mn> <mml:mo>(</mml:mo>...

Abstract We show that all the symmetric projective tensor products of a Banach space X have Daugavet property provided has and either is an $$L_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> -predual (i.e., $$X^{*}$$ <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> isometric to -space) or vector-valued -space. In process proving it, we get number results...

We continue the investigation of behaviour octahedral norms in tensor products Banach spaces. First, we will prove existence a space Y such that injective l1⊗^εY and L1⊗^εY both fail to have an norm, which solves two open problems from literature. Secondly, show presence metric approximation property octahedrality is preserved non-reflexive L-embedded taking projective with arbitrary space.

We characterise the octahedrality of Lipschitz-free space norm in terms a new geometric property underlying metric space. study spaces with and without this property. Quite surprisingly, cannot be embedded isometrically into ℓ 1 similar Banach spaces.

The aim of this note is to study octahedrality in vector-valued Lipschitz-free Banach spaces on a metric space, under topological hypotheses it, by analysing the weak-star strong diameter 2 property Lipschitz function spaces. Also, we show an example that proves our results are optimal and actually relies underlying space as well one.

We study the density of set SNA (M,Y) those Lipschitz maps from a (complete pointed) metric space M to Banach Y which strongly attain their norm (i.e., supremum defining is actually maximum). present new and somehow counterintuitive examples, we give some applications. First, show that (\mathbb T,Y) not dense in Lip _0(\mathbb for any , where \mathbb T denotes unit circle Euclidean plane. This provides first example Gromov concave every molecule exposed point ball Lipschitz-free space) does...

We study Daugavet points and $\Delta $-points in Lipschitz-free Banach spaces. prove that if $M$ is a compact metric space, then $\mu \in S_{\mathcal F(M)}$ point only there no denting of $B_{\mathcal at distance

The aim of this note is to provide several variants the diameter two properties for Banach spaces. We study such looking abundance diametral points, which holds in setting spaces with Daugavet property, example, and we intro- duce spaces, showing these new stability results, inheritance subspaces characterizations terms finite rank projections.

Abstract We study the Daugavet property in tensor products of Banach spaces. show that $L_{1}(\unicode[STIX]{x1D707})\widehat{\otimes }_{\unicode[STIX]{x1D700}}L_{1}(\unicode[STIX]{x1D708})$ has when $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D708}$ are purely non-atomic measures. Also, we $X\widehat{\otimes }_{\unicode[STIX]{x1D70B}}Y$ provided $X$ $Y$ $L_{1}$ -preduals with property, particular, spaces continuous functions this property. With same techniques, also obtain consequences...

We analyse the strong connections between spaces of vector-valued Lipschitz functions and continuous linear operators. apply these links to study duality, Schur properties norm attainment in former class as well their