Related papers: On the generation of Arveson weakly continuous sem…

The famous 1960s Lumer-Phillips Theorem states that a closed and densely defined operator $A\colon D(A)\subseteq X\rightarrow X$ on a Banach space $X$ generates a strongly continuous contraction semigroup if and only if $(A,D(A))$ is…

We investigate spaceability phenomena in linear dynamics from a structural perspective. Given a continuous linear operator \(T:X \to X\), we introduce the set \(\Omega(T)\), consisting of all continuous linear operators \(h:X \to X\) for…

Let $\{A_t\}_{t>0}$ be the dilation group in ${\Bbb R}^n$ generated by the infinitesimal generator $M$ where $A_t=\exp(M\log t)$, and let $\varrho\in C^{\infty}({\Bbb R}^n\setminus\{0\})$ be a $A_t$-homogeneous distance function defined on…

Let $G$ be a locally compact abelian group, and let $\omega:G \to [1,\infty)$ be a measurable weight, i.e., $\omega$ is measurable, and $\omega(s+t)\leq \omega(s)\omega(t)$ for all $s, t \in G$. Let $\mathcal{A}$ be a semisimple commutative…

Given a dense additive subgroup $G$ of $\mathbb R$ containing $\mathbb Z$, we consider its intersection $\mathbb G$ with the interval $[0,1[$ with the induced order and the group structure given by addition modulo $1$. We axiomatize the…

We establish the notion of a ``projective analytic vector'', whose defining requirements are weaker than the usual ones of an analytic vector, and use it to prove generation theorems for one-parameter groups on locally convex spaces. More…

We introduce and investigate a class of ring ideals, termed ring $\mathrm{M}$-ideals, inspired by the Alfsen--Effros theory of $\mathrm{M}$-ideals in Banach spaces. We show that $\mathrm{M}$-ideals extend the classical notion of essential…

We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…

We define new symbol classes for pseudodifferntial operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we…

An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. We concentrate our attention on the separation axioms…

A random vector ${\bf X}$ is weakly stable iff for all $a,b \in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X} + b {\bf X}' \stackrel{d}{=} {\bf X} \Theta$, where $X'$ is an independent copy of $X$ and $\Theta$ is…

In the additive topological group $(\mathbb{R},+)$ of real numbers, we construct families of sets for which elements are not measurable in the Lebesgue sense. The constructed families have algebraic structures of being semigroups (i.e.,…

Let $X$ be a separable Hilbert space endowed with a non-degenerate centred Gaussian measure $\gamma$ and let $\lambda_1$ be the maximum eigenvalue of the covariance operator associated with $\gamma$. The associated Cameron--Martin space is…

Let $\mathfrak{A}$ be a Banach algebra, and $\mathcal{X}$ a Banach $\mathfrak{A}$-bimodule. A bounded linear mapping $\mathcal{D}:\mathfrak{A}\rightarrow \mathcal{X}$ is approximately semi-inner derivation if there eixist nets…

Tensor models admit the large $N$ limit, dominated by the graphs called melons. The melons are characterized by the Gurau number $\varpi=0$ and the amplitude of the Feynman graphs are proportional to $N^{-\varpi}$. Other leading order…

Let $G$ be a locally compact group and $(\Phi,\Psi)$ a complementary pair of Young functions satisfying the $\Delta_2$-condition. Let $A_\Phi(G)$ be the Orlicz analogue of the Fig\`{a}-Talamanca Herz algebra $A_p(G).$ The dual of the…

We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone of a partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and the dominated…

Let $\mathcal{M}$ be a semifinite von Neumann algebra on a Hilbert space $\mathcal{H}$ equipped with a faithful normal semifinite trace $\tau$, $S(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-measurable operators. Let…

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $\tau$ and let $S_0(\tau)$ be the algebra of all $\tau$-compact operators affiliated with $\mathcal{M}$. Let $E(\tau)\subseteq S_0(\tau)$ be a…

Extending M.\ Daws' definition of ultra-amenable Banach algebras, we introduce the notion of operator ultra-amenability for completely contractive Banach algebras. For a locally compact group $G$, we show that the operator ultra-amenability…