unilateral shift
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Shift operator — In mathematics, and in particular functional analysis, the shift operators are examples of linear operators, important for their simplicity and natural occurrence. They are used in diverse areas, such as Hardy spaces, the theory of abelian… … Wikipedia
Wold decomposition — In operator theory, the Wold decomposition, or Wold von Neumann decomposition, is a classification theorem for isometric linear operators on a given Hilbert space. It states that any isometry is a direct sums of copies of the unilateral shift and … Wikipedia
Subnormal operator — In mathematics, especially operator theory, subnormal operators are bounded operators on a Hilbert space defined by weakening the requirements for normal operators. Some examples of subnormal operators are isometries and Toeplitz operators with… … Wikipedia
Weak operator topology — In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space H such that the functional sending an operator T to the complex number is continuous for any… … Wikipedia
Spectrum (functional analysis) — In functional analysis, the concept of the spectrum of a bounded operator is a generalisation of the concept of eigenvalues for matrices. Specifically, a complex number λ is said to be in the spectrum of a bounded linear operator T if… … Wikipedia
Decomposition of spectrum (functional analysis) — In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of… … Wikipedia
Unitary operator — For unitarity in physics, see unitarity (physics). In functional analysis, a branch of mathematics, a unitary operator (not to be confused with a unity operator) is a bounded linear operator U : H → H on a Hilbert space H… … Wikipedia
Strong operator topology — In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map… … Wikipedia
Fuglede's theorem — In mathematics, Fuglede s theorem is a result in operator theory, named after Bent Fuglede. The result Theorem (Fuglede) Let T and N be bounded operators on a complex Hilbert space with N being normal. If TN = NT , then TN* = N*T .Colloquially,… … Wikipedia
Functional calculus — In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. The term was also used previously to refer to the calculus of variations. If f is a function, say a numerical function of a… … Wikipedia
Quasinormal operator — In operator theory, quasinormal operators is a class of bounded operators defined by weakening the requirements of a normal operator. Definition and some properties Definition Let A be a bounded operator on a Hilbert space H , then A is said to… … Wikipedia
