Related papers: A trace formula for functions of contractions and …

We review previous work on spectral flow in connection with certain self-adjoint model operators $\{A(t)\}_{t\in \mathbb{R}}$ on a Hilbert space $\mathcal{H}$, joining endpoints $A_\pm$, and the index of the operator $D_{A}^{}= (d/d t) + A$…

In this paper, we consider the space $\mathrm{BV}^{\mathbb A}(\Omega)$ of functions of bounded $\mathbb A$-variation. For a given first order linear homogeneous differential operator with constant coefficients $\mathbb A$, this is the space…

We develop a Sz.-Nagy--Foias-type functional model for a commutative contractive operator tuple $\underline{T} = (T_1, \dots, T_d)$ having $T = T_1 \cdots T_d$ equal to a completely nonunitary contraction. We identify additional invariants…

An operator $T$ on a Hilbert space $\mathcal H$ is called expansive, if $\|Tx\|\geq \|x\|$ ($x\in\mathcal H$). Expansive operators $T$ quasisimilar to the unilateral shift $S_N$ of finite multiplicity $N$ are studied. It is proved that…

This is a conitunation of [1] and [2]. We prove that if function $f$ belongs to the class $\Lambda_{\omega} \overset{\text{def}}{=} \{f: \omega_{f}(\delta)\leq \text{const} \omega(\delta)\} $ for an arbitrary modulus of continuity $\omega$,…

Some inequalities for quantum f-divergence of trace class operators in Hilbert spaces are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and…

We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by…

We study the functional calculus for operators of the form $f_h(P(h))$ within the theory of semiclassical pseudodifferential operators, where $\{f_h\}_{h\in (0,1]}\subset C^\infty_c(\mathbb{R})$ denotes a family of $h$-dependent functions…

Koplienko [Ko] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert Schmidt class $\bS_2$. A similar formula in the case of unitary operators was obtained by Neidhardt [N]. In this paper we improve their…

By the use of the celebrated Kato's inequality we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space H. Natural applications for functions defined by power series of normal operators are given as…

Let $T$ be a bounded linear operator on a Hilbert space $H$ such that \[ \alpha[T^*,T]:=\sum_{n=0}^\infty \alpha_n T^{*n}T^n\ge 0. \] where $\alpha(t)=\sum_{n=0}^\infty \alpha_n t^n$ is a suitable analytic function in the unit disc…

We show that the space of trace-class operators on a Hilbert module over a commutative C*-algebra, as defined and studied in earlier work of Stern and van Suijlekom (Journal of Functional Analysis, 2021), is completely isometrically…

A general `quantum history theory' can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection…

Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a normal faithful semifinite trace $\tau$, and let $L_p(\mathcal{M})$ denote the associated noncommutative $L_p$-space for $1<p<\infty$. Let $n\in\mathbb{N}$ and let $a, b$…

Answering on the question of S.R.Treil [23], for every $\delta$, $0<\delta<1$, examples of contractions are constructed such that their characteristic functions $F\in H^\infty(\mathcal E\to\mathcal E_\ast)$ satisfy the conditions…

According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L-groups of spherical varieties should give rise to a functorial transfer of…

Let $H(\mathbb{D})$ be the space of all analytic functions in the unit disc $\mathbb{D}$. For $g\in H(\mathbb{D})$, the generalized Hilbert operator $\mathcal{H}_{g}$ is defined by $$\mathcal{H}_{g}(f)(z)=\int_{0}^{1}f(t)g'(tz)dt, \ \ z\in…

For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…

This paper generalizes the classical Sz.-Nagy--Foias $H^{\infty}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1, \dots, T_d)$ of commuting bounded…

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we…