相关论文: Simplicity of reduced group Banach algebras

In this paper, we give some properties of the modulation spaces $M_s^{p,1}({\mathbf R}^n)$ as commutative Banach algebras. In particular, we show the Wiener-L\'evy theorem for $M^{p,1}_s({\mathbf R}^n)$, and clarify the sets of spectral…

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in…

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a…

We prove a number of results linking properties of actions by compact groups (both quantum and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and extensibility of the actions across several constructions.…

Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the $L^p_{\omega}-$conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the…

We prove that, given a discrete group $G$, and $1 \leq p < \infty$, the algebra of $p$-convolution operators $CV_p(G)$ is weak*-simple, in the sense of having no non-trivial weak*-closed ideals, if and only if $G$ is an ICC group. This…

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…

Following results of Bourgain and Gorelik we show that the spaces $\ell_p$, $1<p<\infty$, as well as some related spaces have the following uniqueness property: If $X$ is a Banach space uniformly homeomorphic to one of these spaces then it…

We investigate topologically left Noetherian Banach algebras. We show that if $G$ is a compact group, then $L^{\, 1}(G)$ is topologically left Noetherian if and only if $G$ is metrisable. We prove that, given a Banach space $E$ such that…

Suppose that $G$ is the group of $F$-points of a connected reductive group over $F$, where $F/\mathbb{Q}_p$ is a finite extension. We study the (topological) irreducibility of principal series of $G$ on $p$-adic Banach spaces. For unitary…

We use the compactness theorem of continuous logic to give a new proof that $L^r([0,1]; \mathbb{R})$ isometrically embeds into $L^p([0,1]; \mathbb{R})$ whenever $1 \leq p \leq r \leq 2$. We will also give a proof for the complex case. This…

A theorem of Delorme states that every unitary representation of a connected Lie group with nontrivial reduced first cohomology has a finite-dimensional subrepresentation. More recently Shalom showed that such a property is inherited by…

We introduce and study a new Banach algebra structure on the trace-zero subspace $\mathcal{T}(L^2(\mathbb{G}))_0$ of trace class operators for any locally compact quantum group $\mathbb{G}$; it is defined through a mixed Lie-type product of…

A wide new class of subsets of a Banach space $X$ named coarse $p$-limited sets ($ 1\leq p < \infty$) is introduced by considering weak* $p$-summable sequences in $X'$ instead of weak* null sequences. We study its basic properties and…

If $X$ is an almost transitive Banach space with amenable isometry group (for example, if $X=L^p([0,1])$ with $1\leqslant p<\infty$) and $X$ admits a uniformly continuous map $X\overset\phi\longrightarrow E$ into a Banach space $E$…

We prove that if the group of isometries of C(X,E) is algebraically reflexive, then the group of n-isometries is also algebraically reflexive. Here, X is a compact Hausdorff space and E is a Banach space. As a corollary to this, we…

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot a$ factors through Rosenthal Banach spaces…

We prove that finite-spectrum representations of compact quantum groups either in unital $C^*$-algebras $A$ or on Banach spaces $E$ exhibit the same Banach-space-modeled differential-geometric structure as their classical analogues: (a)…

We introduce the notion of a regular mapping on a non-commutative $L_p$-space associated to a hyperfinite von Neumann algebra for $1\le p\le \infty$. This is a non-commutative generalization of the notion of regular or order bounded map on…