Related papers: Spectrum and convergence of eventually positive op…

This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental…

In this article, we study strictly elliptic, second-order differential operators on a bounded Lipschitz domain in $\mathbb{R}^d$, subject to certain non-local Wentzell-Robin boundary conditions. We prove that such operators generate…

In this brief note we describe relations between the well known notion of a relatively bounded operator and the operator E-norms considered in [arXiv:1806.05668]. We show that the set of all $\sqrt{G}$-bounded operators equipped with the…

In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…

The discrete Ces\`aro operator $\mathsf{C}$ is investigated in the class of power series spaces $\Lambda_0(\alpha)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fr\'echet space…

We study continuity and H\"older continuity of $t\mapsto P_tf$, where $P_t$ is a generalized Mehler semigroup in $C_b(X)$, the space of the continuous and bounded functions from a Banach space $X$ to $R$, and $f\in C_b(X)$. The generators…

Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of…

We show that some abstract results on propagation of fixed points for completely positive maps on $C^*$-algebras provide a natural approach to unify recent Noether type theorems on the equivalence of symmetries with conservation laws for…

We provide a new and significantly shorter optimality proof of recent quantified Tauberian theorems, both in the setting of vector-valued functions and of $C_0$-semigroups, and in fact our results are also more general than those currently…

We study local spectral properties for subordinated operators arising from $C_0$-semigroups. Specifically, if $\mathcal{T}=(T_t)_{t\geq 0}$ is a $C_0$-semigroup acting boundedly on a complex Banach space and $$\mathcal{H}_\nu =…

We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times…

With Charles Read we have introduced and studied a new notion of (real) positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. As motivation note that the `completely'…

Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…

In \cite{Os} a general spectral approximation theory was developed for compact operators on a Banach space which does not require that the operators be self-adjoint and also provides a first order correction term. Here we extend some of the…

Let $X$ be a real or complex Banach space and $T_t:X\to X$ is a power bounded operator (or a $C_0$-semigroup). If there exists a "occasionally" attracting compact subset K (for each x$ in unit ball $\liminf_n \rho(T^n x, K)=0$ then there…

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as…

This paper is a continuation of our paper [Med. J. Math 19, Article number: 31 (2022)] in which we extended the notion of generalized Drazin-Riesz invertible operators to closed operators. We establish here, results relating the notion of…

We give a short new proof of the Arendt-Chernoff-Kato theorem, which characterizes generators of positive C0 semigroups in order unit spaces. The proof avoids half-norms and subdifferentials, and is based on a sufficient condition for an…

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…

The objective of this study is to advance the theory concerning positive summing operators. Our focus lies in examining the space of positive strongly p-summable sequences and the space of positive unconditionally p-summable sequences. We…