operator homomorphism

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• Homomorphism — In abstract algebra, a homomorphism is a structure preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the Greek language: ὁμός (homos) meaning same and μορφή (morphe)… …   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

• Transfer operator — The transfer operator is different from the transfer homomorphism. In mathematics, the transfer operator encodes information about an iterated map and is frequently used to study the behavior of dynamical systems, statistical mechanics, quantum… …   Wikipedia

• Schröder–Bernstein theorems for operator algebras — The Schröder–Bernstein theorem, from set theory, has analogs in the context operator algebras. This article discusses such operator algebraic results. For von Neumann algebras Suppose M is a von Neumann algebra and E , F are projections in M. Let …   Wikipedia

• Interior algebra — In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and… …   Wikipedia

• Holomorphic functional calculus — In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function fnof; of a complex argument z and an operator T , the aim is to construct an operator:f(T),which in a… …   Wikipedia

• Naimark's dilation theorem — In operator theory, Naimark s dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring s dilation theorem. Contents 1 Note 2 Some preliminary notions 3 Naimark s theorem …   Wikipedia

• Semigroup — This article is about the algebraic structure. For applications to differential equations, see C0 semigroup. In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup… …   Wikipedia

• Boolean algebras canonically defined — Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… …   Wikipedia

• Kernel (algebra) — In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a matrix, also… …   Wikipedia

• Structure (mathematical logic) — In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as… …   Wikipedia