Faster access than browser!Similarities between Hahn–Banach theorem and Hilbert space
Hahn–Banach theorem and Hilbert space have 15 things in common (in Unionpedia): Banach space, Bounded operator, Closure (topology), Continuous function, Convex function, Dual space, Functional analysis, Linear form, Linear subspace, Mathematics, Norm (mathematics), Separable space, Topological vector space, Vector space, Zorn's lemma.
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
Banach space and Hahn–Banach theorem · Banach space and Hilbert space ·
Bounded operator
In functional analysis, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless L(v).
Bounded operator and Hahn–Banach theorem · Bounded operator and Hilbert space ·
Closure (topology)
In mathematics, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
Closure (topology) and Hahn–Banach theorem · Closure (topology) and Hilbert space ·
Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
Continuous function and Hahn–Banach theorem · Continuous function and Hilbert space ·
Convex function
In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.
Convex function and Hahn–Banach theorem · Convex function and Hilbert space ·
Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
Dual space and Hahn–Banach theorem · Dual space and Hilbert space ·
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
Functional analysis and Hahn–Banach theorem · Functional analysis and Hilbert space ·
Linear form
In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.
Hahn–Banach theorem and Linear form · Hilbert space and Linear form ·
Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
Hahn–Banach theorem and Linear subspace · Hilbert space and Linear subspace ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Hahn–Banach theorem and Mathematics · Hilbert space and Mathematics ·
Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
Hahn–Banach theorem and Norm (mathematics) · Hilbert space and Norm (mathematics) ·
Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
Hahn–Banach theorem and Separable space · Hilbert space and Separable space ·
Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
Hahn–Banach theorem and Topological vector space · Hilbert space and Topological vector space ·
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
Hahn–Banach theorem and Vector space · Hilbert space and Vector space ·
Zorn's lemma
Zorn's lemma, also known as the Kuratowski–Zorn lemma, after mathematicians Max Zorn and Kazimierz Kuratowski, is a proposition of set theory that states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered subset) necessarily contains at least one maximal element.
Hahn–Banach theorem and Zorn's lemma · Hilbert space and Zorn's lemma ·
The list above answers the following questions
- What Hahn–Banach theorem and Hilbert space have in common
- What are the similarities between Hahn–Banach theorem and Hilbert space
Hahn–Banach theorem and Hilbert space Comparison
Hahn–Banach theorem has 42 relations, while Hilbert space has 298. As they have in common 15, the Jaccard index is 4.41% = 15 / (42 + 298).
References
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