Related papers: A Gelfand-Naimark type theorem

Let $X$ be a complex Banach space and let $J:X \to X^*$ be a duality section on $X$ (i.e. $\langle x,J(x)\rangle=\|J(x)\|\|x\|=\|J(x)\|^2=\|x\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\{e^{tA}:t \geq 0\}$,…

For a bounded function $f$ from the unit sphere of a closed subspace $X$ of a Banach space $Y$, we study when the closed convex hull of its spatial numerical range $W(f)$ is equal to its intrinsic numerical range $V(f)$. We show that for…

It is shown that a separable Banach space $X$ can be given an equivalent norm $|\!|\!|\cdot |\!|\!|$ with the following properties:\quad If $(x_n)\subseteq X$ is relatively weakly compact and $\lim_{m\to\infty} \lim_{n\to\infty}\break…

Let $X$ and $Y$ be completely regular spaces and $E$ and $F$ be Hausdorff topological vector spaces. We call a linear map $T$ from a subspace of $C(X,E)$ into $C(Y,F)$ a \emph{Banach-Stone map} if it has the form $Tf(y) = S_{y}(f(h(y))$ for…

Let G be a connected semisimple linear algebraic group over an algebraically closed field k of positive characteristic and let X denote an equivariant embedding of G. We define a distinguished Steinberg fiber N in G, called the zero-fiber,…

We describe the compact objects in the $\infty$-category of $\mathcal C$-valued sheaves $\text{Shv} (X,\mathcal C)$ on a hypercomplete locally compact Hausdorff space $X$, for $\mathcal C$ a compactly generated stable $\infty$-category.…

For each $n \in \mathbb{N}$ a Banach space $\mathfrak{X}_{0,1}^n$ is constructed is having the property that every normalized weakly null sequence generates either a $c_0$ or $\ell_1$ spreading models and every infinite dimensional subspace…

We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded $\alpha$-twisted derivations and almost periodic elements. Under natural continuity and compactness assumptions, we establish a complete…

In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any…

Consider a continuous bundle $\mathcal{E}\to X$ of Banach/Hilbert spaces or Banach/$C^*$-algebras over a paracompact base space, equivariant for a compact Lie group $\mathbb{U}$ operating on all structures involved. We prove that in all…

Let $({\sf G},\alpha, \omega,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is…

We investigate the quotients of Banach manifolds with respect to free actions of pseudogroups of local diffeomorphisms. These quotient spaces are called H-manifolds since the corresponding simply transitive action of the pseudogroup on its…

It is shown that if the Deddens algebra ${\mathcal D}_T$ associated with a quasinilpotent operator $T$ on a complex Banach space is closed and localizing then $T$ has a nontrivial closed hyperinvariant subspace.

Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $\Phi$. We consider a Riesz type factorization theorem in noncommutative $H^p$…

We study the closed algebra B_I(G) generated by the idempotents in the Fourier-Stieltjes algebra of a locally compact group G. We show that it is a regular Banach algebra with computable spectrum G^I, which we call the idempotent…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

Let $X$ be a Hausdorff space and let $\mathcal{H}$ be one of the hyperspaces $CL(X)$, $\mathcal{K}(X)$, $\mathcal{F}(X)$ or $\mathcal{F}_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness…

We introduce a decreasing one-parameter family $\mathfrak{X}^{\gamma}(M)$, $\gamma>0$, of Banach subspaces of the Hardy-Goldberg space $\mathfrak{h}^1(M)$ on certain nondoubling Riemannian manifolds with bounded geometry and we investigate…

If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers.…

We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset \mathcal{F} of X^{\ast}, which separates X, there exists a countable separating subset \mathcal{F}_{0} of…