PlanetMath: H * -algebra

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H * -algebra

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H *-algebra

An H $*$ -algebra is defined as a Hilbert space $\mathbb{A}_H$ equipped with an associative unital algebra structure and an antilinear involution $^*:\mathbb{A}_H \to \mathbb{A}_H$ which is compatible with taking the adjoint of the operators on the Hilbert space for the left and right multiplication of $\mathbb{A}_H$ with itself (ref. [1]).

"H * -algebra" is owned by bci1.

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Keywords:

Hilbert involutive algebra, operator and adjoint operator

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Cross-references: multiplication, right, operators, adjoint, compatible, involution, structure, algebra, unital, associative, Hilbert space
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This is version 4 of H * -algebra, born on 2008-09-28, modified 2009-02-01.
Object id is 11102, canonical name is HAlgebra.
Accessed 492 times total.

Classification:

AMS MSC:	81R15 (Quantum theory :: Groups and algebras in quantum theory :: Operator algebra methods)
	81R05 (Quantum theory :: Groups and algebras in quantum theory :: Finite-dimensional groups and algebras motivated by physics and their representations)
	20G42 (Group theory and generalizations :: Linear algebraic groups :: Quantum groups and their representations)
	46N50 (Functional analysis :: Miscellaneous applications of functional analysis :: Applications in quantum physics)

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