Related papers: Stability of linear GMRES convergence with respect…

Here I give a direct proof that smooth curves with distinct marked points are asymptotically Hilbert stable with respect to a wide range of parameter spaces and linearizations. This result can be used to construct the coarse moduli space of…

We prove that a generic canonically or bicanonically embedded smooth curve has semistable m-th Hilbert points for all m. We also prove that a generic bicanonically embedded smooth curve has stable m-th Hilbert points for all m \geq 3. In…

We give sufficient conditions for the essential self-adjointness of perturbed biharmonic operators acting on sections of a Hermitian vector bundle over a Riemannian manifold with additional assumptions, such as lower semi-bounded Ricci…

Let $\A$ and $\B$ be operator algebras with $c_0$-isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically isomorphic, then $\A$ and $\B$ are isometrically isomorphic.…

Let $H_0$ be a self-adjoint operator on a Hilbert space $\mathcal H$ endowed with a rigging $F,$ which is a zero-kernel closed operator from $\mathcal H$ to another Hilbert space $\mathcal K$ such that the sandwiched resolvent $F (H_0 -…

Let $f \geq 0$ be operator monotone on $[0, \infty)$. In this paper we prove that for any unitarily-invariant norm $|||-|||$ on $M_n(\mathbb{C})$ and matrices $A, B, X \in M_n(\mathbb{C})$ with $A, B \geq 0$ and $|||X||| \leq 1$,…

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…

We answer a question of Peller by showing that for any c>1 there exists a power-bounded operator T on a Hilbert space with the property that any operator S similar to T satisfies $\sup_n\|S^n\|>c.$

Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

Consider a compact Lie group $G$ and a closed subgroup $H<G$. Suppose $\mathcal M$ is the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. We obtain a sufficient condition for the existence of $g\in\mathcal M$ and…

The conditions for sequences $\{f_{k}\}_{k=1}^{\infty}$ and $\{g_{k}\}_{k=1}^{\infty}$ being Bessel sequences, frames or Riesz bases, can be expressed in terms of the so-called cross-Gram matrix. In this paper we investigate the cross-Gram…

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…

This paper studies strict fixed point and stability results for multivalued operators which does not satisfy a \'Ciri\'c type contraction condition, but their admissible perturbation does. We focus on the conditions imposed on the…

Let $B$, $I$ be the unweighted backward shift and the identity operator respectively on $l^{\infty}(\mathbb{N})$, the space of bounded sequences over the complex numbers endowed with the supremum norm. We prove that $I+\lambda B$ is locally…

Motivated by a spectral analysis of the generator of completely positive trace-preserving semigroup, we analyze a real functional $$ A,B \in M_n(\mathbb{C}) \to r(A,B) = \frac{1}{2}\Bigl(\langle [B,A],BA\rangle + \langle [B,A^\ast],BA^\ast…

Motivated by Arveson's conjecture, we introduce a notion of hyperrigidity for a partial order on the state space of a $C^*$-algebra $B$. We show how this property is equivalent to the existence of a boundary: a subset of the pure states…

We provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability…

New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, non-Hermitian linear systems. These bounds are given for the case when the Hermitian part of the coefficient matrix is…

The paper deals with initial-boundary value problems for the linear wave equation whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^2$ under small…