Related papers: Can you compute the operator norm?

We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…

A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…

Let $\mathbb{H}$ be a separable Hilbert space. In this paper we establish a generalization of Walnut's representation and Janssen's representation of the $\mathbb{H}-$valued Gabor frame operator on $\mathbb{H}-$valued weighted amalgam…

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

A bounded operator on a real or complex separable infinite-dimensional Banach space $Z$ is universal in the sense of Glasner and Weiss if for every invertible ergodic measure-preserving transformation $T$ of a standard Lebesgue probability…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

Families of operator identities appeared as a consequence of an existence of finite-dimensional representation of (super) Lie algebras of first-order differential operators and $q$-deformed (quantum) algebras of first-order…

Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite…

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.

In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete…

Let $ \mathbb{B}(\mathscr{H})$ represent the $C^*$-algebra, which consists of all bounded linear operators on $\mathscr{H},$ and let $N ( .) $ be a norm on $ \mathbb{B}(\mathscr{H})$. We define a norm $w_{(N,e)} (. , . )$ on $…

We use non-standard analysis to define a category $^\star\!\operatorname{Hilb}$ suitable for categorical quantum mechanics in arbitrary separable Hilbert spaces, and we show that standard bounded operators can be suitably embedded in it. We…

We compute the exact value of the essential norm of a generalized Hilbert matrix operator acting on weighted Bergman spaces $A^p_v$ and weighted Banach spaces $H^\infty_v$ of analytic functions, where $v$ is a general radial weight. In…

For $q>0$ let $\cA$ denote the unital $\ast$-algebra with generator $x$ and defining relation $xx^\ast=qxx^\ast$. Based on this algebra we study $q$-normal operators, the complex $q$-moment problem, positive elements and sums of squares.

The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…

Let $X$ be a right Hilbert module over a $C^*$-algebra $A$ equipped with the canonical operator space structure. We define an elementary operator on $X$ as a map $\phi : X \to X$ for which there exists a finite number of elements $u_i$ in…

The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real…