Related papers: Extended Rako\v{c}evi\'{c}'s property

We extend and study the notion of bounded point evaluation introduced by Williams for a cyclic operator to the class of operators with the wandering subspace property. We characterize the set $bpe(T)$ of all bounded point evaluations for an…

It is well known that functions (resp. operators) satisfying a property~$p$ on a subset $Q\subset \mathbb{R}^d$ cannot necessarily be extended to a function (resp. operator) satisfying~$p$ on the whole of~$\mathbb{R}^d$. Given $Q \subseteq…

In this article, we show that a commuting pair $T=(T_1,T_2)$ of $\ast$-paranormal operators $T_1$ and $T_2$ with quasitriangular property satisfy the Weyl's theorem-I, that is $$\sigma_T(T)\setminus\sigma_{T_W}(T)=\pi_{00}(T)$$ and a…

We study Birkhoff-James orthogonality of bounded linear operators on complex Banach spaces and obtain a complete characterization of the same. By means of introducing new definitions, we illustrate that it is possible in the complex case,…

For a proper function $f$ on the plane, we study the operator \[ Tf(x,y) = \lim_{\varepsilon\to 0} \int_\varepsilon^1 f(x-t,y-t^k) \frac{e^{2\pi i \gamma(t)}}{\psi(t)} dt, \] where $k\ge1$ and $\psi$ and $\gamma$ are functions defined near…

The Coifman-Fefferman inequality implies quite easily that a Calderon-Zygmund operator $T$ acts boundedly in a Banach lattice $X$ on $\mathbb R^n$ if the Hardy-Littlewood maximal operator $M$ is bounded in both $X$ and $X'$. We discuss this…

In [Math. Ineq. \& appl., Vol 26 (2) (2023), 511-530] and [Period. Math. Hung., 89 (1) (2024), 116-128], the present author proved that the Riesz potential $I_{\alpha}$ extends to a bounded operator $H^{p(\cdot)}_{\omega}(\mathbb{R}^n) \to…

Let (M,N) be a pair of von Neumann algebras, or of dual operator spaces with at least one of them having property S_\sigma, and let T be an arbitrary completely bounded mapping on M. We present an explicit construction of an amplification…

We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…

Let $W_0(\mathbb R)$ be the Wiener Banach algebra of functions representable by the Fourier integrals of Lebesgue integrable functions. It is proven in the paper that, in particular, a trigonometric series $\sum\limits_{k=-\infty}^\infty…

In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

Let $T$ be a bounded linear operator on a complex Hilbert space $\mathscr{H}.$ We obtain various lower and upper bounds for the numerical radius of $T$ by developing the Euclidean operator radius bounds of a pair of operators, which are…

Following Berm\'udez et al. (ArXiv: 1706.03638v1), we study the rate of growth of the norms of the powers of a linear operator, under various resolvent conditions or Ces\`aro boundedness assumptions. We show that $T$ is power-bounded if…

For a closed densely defined operator $T$ from a Hilbert space $\mathfrak{H}$ to a Hilbert space $\mathfrak{K}$, necessary and sufficient conditions are established for the factorization of $T$ with a bounded nonnegative operator $X$ on…

We prove the Bari-Markus property for spectral projectors of non-self-adjoint Dirac operators on a finite interval with square-integrable matrix-valued potentials and some separated boundary conditions.

This paper studies a zeta function of two complex variables (w, s) attached to an algebraic number field K, introduced by van der Geer and Schoof, which is based on an analogue of the Riemann-Roch theorem for number fields using Arakelov…

Borg-type uniqueness theorems for matrix-valued Jacobi operators H and supersymmetric Dirac difference operators D are proved. More precisely, assuming reflectionless matrix coefficients A, B in the self-adjoint Jacobi operator H=AS^+ +…

We study orthogonally additive operators between Riesz spaces without the Dedekind completeness assumption on the range space. Our first result gives necessary and sufficient conditions on a pair of Riesz spaces $(E,F)$ for which every…

We develop a new refinement of the Kato's inequality and using this refinement we obtain several upper bounds for the numerical radius of a bounded linear operator as well as the product of operators, which improve the well known existing…