Related papers: A Generalized Spectral Radius Formula and Olsen's …

In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of starlike and convex analytic functions. We also obtain the Bohr…

In this paper, we try to minimize the scope of possible unique metric spectra up to equivalence. While it is well known that every spectra $S\subseteq \mathbb{R}^+$ is equivalent to a spectra $T\subseteq \mathbb{N}$, it has remained open if…

We extend Friedman's theorem to show that, for any fixed $r>1$, a random $2r$--regular Schreier graph associated with the action of $r$ uniformly random permutations of $[n]$ on $k_{n}$--tuples of distinct elements in $[n]$ has a…

The $p$-spectral radius of a graph $G=(V,E)$ with adjacency matrix $A$ is defined as $\lambda^{(p)}(G)=\max \{x^TAx : \|x\|_p=1 \}$. This parameter shows remarkable connections with graph invariants, and has been used to generalize some…

Building on the work of \.{I}nan and of Almahariq--Peters--Vergili, we develop an axiomatic framework for approximate algebra based on an algebra-compatible closure operator $\Phi^{\!*}$ on a unital ring. The operator is assumed to be…

Recall that the radius of a compact metric space $(X, dist)$ is given by $rad\ X = \min_{x\in X} \max_{y\in X} dist(x,y)$. In this paper we generalize Berger's $\frac{1}{4}$-pinched rigidity theorem and show that a closed, simply connected,…

Let $A\in\mathbb{C}^{n\times n}$ be a normal matrix with spectrum $\{\lambda_{i}\}_{i=1}^{n}$, and let $\widetilde{A}=A+E\in\mathbb{C}^{n\times n}$ be a perturbed matrix with spectrum $\{\widetilde{\lambda}_{i}\}_{i=1}^{n}$. If…

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…

The authors consider the class $\F$ of normalized functions $f$ analytic in the unit disk $\ID$ and satisfying the condition $${\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2},\quad z\in\D. $$ Recently, Ponnusamy et al.…

The paper deals with spectral order isomorphisms in the framework of AW*-algebras. We establish that every spectral order isomorphism between sets of all self-adjoint operators (or between sets of all effects, or between sets of all…

We give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of Hilbert function spaces on the ball, and obtain norm bounds analogous to the standard one-variable…

For $r\geq 2$ and $p\geq 1$, the $p$-spectral radius of an $r$-uniform hypergraph $H=(V,E)$ on $n$ vertices is defined to be $$\rho_p(H)=\max_{{\bf x}\in \mathbb{R}^n: \|{\bf x}\|_p=1}r \cdot \!\!\!\! \sum_{\{i_1,i_2,\ldots, i_r\}\in E(H)}…

Let $A$ be a $0$-sectorial operator with a bounded $H^\infty(\Sigma\_\sigma)$-calculus for some $\sigma \in (0,\pi),$ e.g. a Laplace type operator on $L^p(\Omega),\: 1 < p < \infty,$ where $\Omega$ is a manifold or a graph. We show that $A$…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

Let $G$ be a finite abelian group of order $n$ and let $\Delta_{n-1}$ denote the $(n-1)$-simplex on the vertex set $G$. The sum complex $X_{A,k}$ associated to a subset $A \subset G$ and $k < n$, is the $k$-dimensional simplicial complex…

Here we develop a regularity theory for a polyconvex functional in $2\times2-$dimensional compressible finite elasticity. In particular, we consider energy minimizers/stationary points of the functional…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

For $r\geq 3$, let $f_r\colon [0,\infty)\to [1,\infty)$ be the unique analytic function such that $f_r({k\choose r})={k-1\choose r-1}$ for any $k\geq r-1$. We prove that the spectral radius of an $r$-uniform hypergraph $H$ with $e$ edges is…

We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…

We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate how these commutative spectra can be functorially ``sewn…