Operator topology
Operator topology In mathematics, the requirements of functional analysis ... to T in the uniform operator topology. If $T\_n\; x\; \backslash to\; Tx$ in the strong operator topology. Finally, suppose $T\_n\; x\; \backslash to\; Tx$ in the weak topology of H. This means that $F\; ...\; to\; T$ in the weak operator topology. All of these notions make sense ...
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Weak topology
Weak topology In mathematics, weak topology is an alternative term for initial topology. The term is most commonly used for the initial topology of a normed vector space with respect ... vector space X is, by using the norm to measure distances, a metric space ...
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Norm (mathematics)
Norm (mathematics) In linear algebra, functional analysis and related areas of mathematics, a norm is a function which assigns a positive ... other than the zero vector. A semi-norm on the other hand is allowed to ... space R 2 equipped with the Euclidean norm. Elements in this vector space (e.g ... at the origin (0,0). The Euclidean norm assigns to each vector the length ...
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Ultrastrong topology
Ultrastrong topology In functional analysis, the ultrastrong topology, or σ-strong topology on the set B(H) of bounded ... operators on a Hilbert space is the topology defined by the family of seminorms p ... 1/2 .) Relation with the strong (operator) topology The ultrastrong topology is similar to ...
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Ultraweak topology
Ultraweak topology In functional analysis, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, on the set B(H) of ...
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Polar topology
Polar topology In functional analysis and related areas of mathematics a polar topology, topology of $\backslash mathcal\{A\}$-convergence or topology of uniform convergence on the sets of ... subset of $Y$, the polar topology on $Y$ is defined ...
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Matrix norm
Matrix norm In mathematics, the term matrix norm can have two meanings: A vector norm on matrices, i.e, a norm on the vector space of all real ... by-n matrices. A sub-multiplicative vector norm is any vector norm on square ...
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Strong topology
Strong topology In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different ... context, and it may refer to: the topology arising from a norm the strong ...
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Talk:Norm (mathematics)
Talk:Norm (mathematics) Does anyone know what the modulus ... also write f(x), with f the norm and x an element of the vector space V. The properties of the norm function are given in the article. I ... 13:33, 29 Oct 2004 (UTC) Merging norm (mathematics) and normed vector space Would it ... learn about the other as well. the topology induced by a norm is currently ...
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Strong operator topology
Strong operator topology In functional analysis, the strong operator topology, often abbreviated SOT, is the weakest topology on the set of bounded operators on ... SOT is stronger than the weak operator topology and weaker than the norm topology. The SOT lacks some of ...
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