Related papers: Averaged wave operators and complex-symmetric oper…

We consider averaged wave operators constructed for singular unitary operators $U_1$, $U_2$ and a bounded identification operator $A$. In the case of rank-two commutator $AU_1 - U_2A$, we show that averaged wave operators of past and future…

We study the spectral behavior as the sample size $n \to +\infty$ of integral operators defined by convolution of a non-negative symmetric kernel k with respect to empirical measures $\mu_n = \frac{1}{n} \sum_{i=1}^n \delta_{X_i}$, where…

We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some…

We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures $\mu_n$ on $\mathbb R$. If this sequence of operators constitutes an approximate identity on a particular class of…

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…

We consider sequences of operators $U_n:L^1(X)\to M(X)$, where $X$ is a space of homogeneous type. Under certain conditions on the operators $U_n$ we give a complete characterization of convergence (divergence) sets of functional sequences…

Let $\mathcal{M}\subseteq\mathcal{B}\left( \mathcal{H}\right) $ be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight $\tau$ where $\mathcal{B}\left( \mathcal{H}\right) $ is the…

We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…

Let M_n be the collection of n x n complex matrices equipped with operator norm. Suppose U, V \in M_n are two unitary matrices, each possessing a gap larger than \Delta in their spectrum, which satisfy ||UV-VU|| \le \epsilon. Then it is…

It was shown by M. I. Zelikin (2007) that the spectrum of a nuclear operator in a separable Hilbert space is central-symmetric iff the spectral traces of all odd powers of the operator equal zero. The criterium can not be extended to the…

Certain Bernoulli convolution measures (\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be…

We prove a general weak existence theorem for wave operators for hybrid normed ideal perturbations. We then use this result to prove the invariance of Lebesgue absolutely continuous parts of n-tuples of commuting hermitian operators under…

Let $U$ be a unitary operator acting on the Hilbert space $H$, $\a:\{1,..., 2k\}\mapsto\{1,..., k\}$ a pair--partition, and finally $A_{1},...,A_{2k-1}\in B(H)$. We show that the ergodic average $$…

For every $n>0$ there is a unitary operator $U$ such that the unitary operator with simple Lebesgue spectrum is isomorphic to the tensor product $U\otimes U^2\otimes\dots\otimes U^{2^n}.$ There is an ergodic automorphism $T$ with its…

We study pairs $(U,L_0)$, where $U$ is a unitary operator in $H$ and $L_0\subset H$ is a closed subspace, such that $$ P_{L_0}U|_{L_0}:L_0\to L_0 $$ has a singular value decomposition. Abstract characterizations of this condition are given,…

Let $L_0$ be a closed densely defined symmetric semi-bounded operator with nonzero defect indexes in a separable Hilbert space ${\cal H}$. With $L_0$ we associate a metric space $\Omega_{L_0}$ that is named a {\it wave spectrum} and…

Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…

We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.