Related papers: The Daugavet property and translation-invariant su…

We define a notion of Property (T) for an arbitrary $C^*$-algebra $A$ admitting a tracial state. We extend this to a notion of Property (T) for the pair $(A,B),$ where $B$ is a $C^*$-subalgebra of $A.$ Let $\Gamma$ be a discrete group and…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also a complex manifold satisfying a local subelliptic estimate. In this work, we show…

We prove that if a metric space $M$ has the finite CEP then $\mathcal F(M)\widehat{\otimes}_{\pi} X$ has the Daugavet property for every non-zero Banach space $X$. This applies, for instance, if $M$ is a Banach space whose dual is…

Let $D \subseteq A$ be a quasi-Cartan pair of algebras. Then there exists a unique discrete groupoid twist $\Sigma \to G$ whose twisted Steinberg algebra is isomorphic to $A$ in a way that preserves $D$. In this paper, we show there is a…

Let $\Gamma$ be a countable discrete group. We say that $\Gamma$ has $C^*$-invariant subalgebra rigidity (ISR) property if every $\Gamma$-invariant $C^*$-subalgebra $\mathcal{A}\le C_r^*(\Gamma)$ is of the form $C_r^*(N)$ for some normal…

Let $\mathcal G\subset L^2(\mathbb R)$ be the subspace spanned by a Gabor Riesz sequence $(g,\Lambda)$ with $g\in L^2(\mathbb R)$ and a lattice $\Lambda\subset\mathbb R^2$ of rational density. It was shown recently that if $g$ is…

We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm.

Let $G$ and $\tilde G$ be connected complex reductive Lie groups, $G$ semisimple. Let $\Lambda^+$ be the monoid of dominant weights for a positive root system $\Delta^+$, and let $l(w)$ be the length of a Weyl group element $w$. Let…

We introduce the super alternative Daugavet property (super ADP) which lies strictly between the Daugavet property and the Alternative Daugavet property as follows. A Banach space $X$ has the super ADP if for every element $x$ in the unit…

Let $M$ be a smooth compact manifold and $\Lambda$ be a compact invariant set. In this paper we prove that for every robustly transitive set $\Lambda$, $f|_\Lambda$ satisfies a $C^1-$generic-stable shadowable property (resp.,…

We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

Let $G$ be a countable group. We introduce several equivalence relations on the set ${\rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $\lambda_{G/H}$ associated to $H\in {\rm Sub}(G)$ and compare…

Consider $(G, V)$ a finite-dimensional representation of a connected reductive complex Lie group $G$ and $\mathbb{P}\left( V\right) $ the projective space of $V$. Denote by $G'$ the derived subgroup of $G$ and assume that the categorical…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also a strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts by…

We study the Daugavet property in the space of Lipschitz functions $\operatorname{Lip}_0(M)$ for a complete metric space $M$. Namely we show that $\operatorname{Lip}_0(M)$ has the Daugavet property if and only if $M$ is a length space. This…

We give a characterisation of the separable Banach spaces with the Daugavet property which is applied to study the Daugavet property in the projective tensor product of an $L$-embedded space with another non-zero Banach space. The former…

Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation lambda_{G/H} of G on L^2(G/H) has a spectral gap, that is, the restriction of lambda_{G/H} to…

A subset of a discrete group $G$ is called completely Sidon if its span in $C^*(G)$ is completely isomorphic to the operator space version of the space $\ell_1$ (i.e. $\ell_1$ equipped with its maximal operator space structure). We recently…

We show that $L^p$-spaces over atomless measure spaces can be characterized in terms of a $p$-concavity type geometric property that is related with the Daugavet property.

Let $G$ be a semisimple adjoint group over $\bold C$ and $\bar{G}$ be the De Concini-Procesi completion of $G$. In this paper, we define a Lagrangian subvariety $\Lambda$ of the cotangent bundle of $\bar{G}$ such that the singular support…