In functional analysis, a reflexive operator algebraA is an operator algebra that has enough invariant subspaces to characterize it. Formally, A is reflexive if it is equal to the algebra of bounded operators which leave invariant each subspace left invariant by every operator in A.
This should not be confused with a reflexive space.
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analysis, a reflexiveoperatoralgebra A is an operatoralgebra that has enough invariant subspaces to characterize it. Formally, A is reflexive if it is...
relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset". It is the algebra of the set-theoretic operations...
in particular, that every non-reflexive Banach space has some bounded linear functional (a type of bounded linear operator) that does not achieve its norm...
properties. They are non-selfadjoint algebras, are closed in the weak operator topology and are reflexive. Nest algebras are among the simplest examples of...
Finitary closure operators with this property give rise to antimatroids. As another example of a closure operator used in algebra, if some algebra has universe...
Arveson, W. (1976). An Invitation to C*-Algebra. Springer-Verlag. ISBN 0-387-90176-0. R. C. James (1951). "A non-reflexive Banach space isometric with its second...
In analogy with the case of the algebraic double dual, there is always a naturally defined continuous linear operator Ψ : V → V′′ from a normed space...
of algebra, every linear operator on a nonzero finite-dimensional complex vector space has an eigenvector. Therefore, every such linear operator in at...
Compact operators on a Banach space are always completely continuous. If X is a reflexive Banach space, then every completely continuous operator T : X...
Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector...
algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator....
In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities...
conditional Minimal axioms for Boolean algebra Peirce arrow Read-once function Sheffer stroke Sole sufficient operator Symmetric Boolean function Symmetric...
complete Heyting algebra (or "frame" or "locale"). Filters and nets are notions closely related to order theory and the closure operator of sets can be...
In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the...
have are: Reflexive: for all x ∈ X , {\displaystyle x\in X,} x R x {\displaystyle xRx} . For example, ≥ {\displaystyle \geq } is a reflexive relation but...
its reflexive reduction <). Complete Boolean algebra. A Boolean algebra that is a complete lattice. Complete Heyting algebra. A Heyting algebra that...
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...
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