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operator topology

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  • Operator topology — In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H. Contents 1 Introduction 2 List of topologies on B(H) 3 …   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

  • 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

  • Operator algebra — In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional… …   Wikipedia

  • Operator product expansion — Contents 1 2D Euclidean quantum field theory 2 General 3 See also 4 External links 2D Euclidean quantum field theory …   Wikipedia

  • Operator norm — In mathematics, the operator norm is a means to measure the size of certain linear operators. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces. Contents 1 Introduction and definition 2 …   Wikipedia

  • Operator K-theory — In mathematics, operator K theory is a variant of K theory on the category of Banach algebras (In most applications, these Banach algebras are C* algebras). Its basic feature that distinguishes it from algebraic K theory is that it has a Bott… …   Wikipedia

  • Ultrastrong topology — In functional analysis, the ultrastrong topology, or sigma; strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the family of seminorms pw(x) for positive elements w of the… …   Wikipedia

  • Weak topology — This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology. For the weak topology generated by a cover of a space see coherent topology. In mathematics, weak topology… …   Wikipedia

  • Ultraweak topology — In functional analysis, a branch of mathematics, the ultraweak topology, also called the weak * topology, or weak * operator topology or sigma; weak topology, on the set B ( H ) of bounded operators on a Hilbert space is the weak * topology… …   Wikipedia

  • Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia

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