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Borel functional calculus and Hilbert space

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Borel functional calculus and Hilbert space

Borel functional calculus vs. Hilbert space

In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectra), which has particularly broad scope. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

Similarities between Borel functional calculus and Hilbert space

Borel functional calculus and Hilbert space have 13 things in common (in Unionpedia): Continuous functional calculus, Eigenvalues and eigenvectors, Functional analysis, Hamiltonian (quantum mechanics), Inner product space, Laplace operator, Mathematics, Measure (mathematics), Observable, Orthonormal basis, Quantum mechanics, Self-adjoint operator, Von Neumann algebra.

Continuous functional calculus

In mathematics, particularly in operator theory and C*-algebra theory, a continuous functional calculus is a functional calculus which allows the application of a continuous function to normal elements of a C*-algebra.

Borel functional calculus and Continuous functional calculus · Continuous functional calculus and Hilbert space · See more »

Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

Borel functional calculus and Eigenvalues and eigenvectors · Eigenvalues and eigenvectors and Hilbert space · See more »

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.

Borel functional calculus and Functional analysis · Functional analysis and Hilbert space · See more »

Hamiltonian (quantum mechanics)

In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.

Borel functional calculus and Hamiltonian (quantum mechanics) · Hamiltonian (quantum mechanics) and Hilbert space · See more »

Inner product space

In linear algebra, an inner product space is a vector space with an additional structure called an inner product.

Borel functional calculus and Inner product space · Hilbert space and Inner product space · See more »

Laplace operator

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.

Borel functional calculus and Laplace operator · Hilbert space and Laplace operator · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Borel functional calculus and Mathematics · Hilbert space and Mathematics · See more »

Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

Borel functional calculus and Measure (mathematics) · Hilbert space and Measure (mathematics) · See more »

Observable

In physics, an observable is a dynamic variable that can be measured.

Borel functional calculus and Observable · Hilbert space and Observable · See more »

Orthonormal basis

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.

Borel functional calculus and Orthonormal basis · Hilbert space and Orthonormal basis · See more »

Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

Borel functional calculus and Quantum mechanics · Hilbert space and Quantum mechanics · See more »

Self-adjoint operator

In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.

Borel functional calculus and Self-adjoint operator · Hilbert space and Self-adjoint operator · See more »

Von Neumann algebra

In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator.

Borel functional calculus and Von Neumann algebra · Hilbert space and Von Neumann algebra · See more »

The list above answers the following questions

Borel functional calculus and Hilbert space Comparison

Borel functional calculus has 37 relations, while Hilbert space has 298. As they have in common 13, the Jaccard index is 3.88% = 13 / (37 + 298).

References

This article shows the relationship between Borel functional calculus and Hilbert space. To access each article from which the information was extracted, please visit:

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