mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

generalization of spectral theory of a single operator. In general, operator algebras are non-commutative rings. An operator algebra is typically required...

their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions...

Integral Equations and Operator Theory is a journal dedicated to operator theory and its applications to engineering and other mathematical sciences....

of the theory of compact operators is in the theory of integral equations, where integral operators supply concrete examples of such operators. A typical...

In functional analysis and operator theory, a bounded linear operator is a special kind of linear transformation that is particularly important in infinite...

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential...

particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x ↦ f(x) to its translation...

In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the...

Subnormal operators Continuous linear operator – Function between topological vector spaces Contraction (operator theory) – Bounded operators with sub-unit...

In operator theory, a bounded operator T on a Banach space is said to be nilpotent if Tn = 0 for some positive integer n. It is said to be quasinilpotent...

In operator theory, a multiplication operator is a linear operator Tf defined on some vector space of functions and whose value at a function φ is given...

mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it...

continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed...

finite}}\right\}.} In the theory of partially ordered sets, which are important in theoretical computer science, closure operators have a more general definition...

entries. In operator theory, particularly the study of PDEs, operators are particularly easy to understand and PDEs easy to solve if the operator is diagonal...

In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

left-adjoint of the transfer operator of Frobenius–Perron. Using the language of category theory, the composition operator is a pull-back on the space...

and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation...

pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial...

In mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar...

In mathematics, a self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear...

mathematics, operator K-theory is a noncommutative analogue of topological K-theory for Banach algebras with most applications used for C*-algebras. Operator K-theory...

classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory. They play a central...

specifically in operator theory, each linear operator A {\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle...

compact operators. The reader will see that most statements transfer verbatim from the matrix case. The spectral theory of compact operators was first...

In operator theory, a bounded operator T: X → Y between normed vector spaces X and Y is said to be a contraction if its operator norm ||T || ≤ 1. This...

defined by convex open sets Operator theory – Mathematical field of study Operator topologies – Topologies on the set of operators on a Hilbert space Quantum...

h(x)=1/x-\lfloor 1/x\rfloor } is called the Gauss–Kuzmin–Wirsing (GKW) operator. The theory of the GKW dates back to a hypothesis by Gauss on continued fractions...

Hessenberg matrices for the Bergman shift operator on Jordan regions". Complex Analysis and Operator Theory. 8 (1): 1–24. arXiv:1205.4183. doi:10.1007/s11785-012-0252-8...