Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the algebraic, geometric, and analytic structure of the set of idempotent elements in a real or complex Banach algebra is studied, and it is shown that a neighborhood of each ideme-potent in the Set of Idempotents in a Rees product subsemigroup is a generalized saddle, a type of analytic manifold.
Abstract: We study here the algebraic, geometric, and analytic structure of the set of idempotent elements in a real or complex Banach algebra. A neighborhood of each idempotent in the set of idempotents forms the set of idempotents in a Rees product subsemigroup of the Banach algebra. Each nontrivial connected component of the set of idempotents is shown to be a generalized saddle, a type of analytic manifold. Each component is also shown to be the quotient of a (possibly infinite dimensional) Lie group by a Lie subgroup.
8 citations
01 Jan 2002
TL;DR: In this paper, it was shown that the product PA = AA + is the orthogonal projector on the range (column space) of A, where A+ is the Moore-Penrose inverse of A; which is the unique solution of the following four Penrose equations.
Abstract: A complex square matrix A is said to be idempotent, or a projector, whenever A2 = A; when A is idempotent, and Hermitian (or real symmetric), it is often called an orthogonal projector, otherwise an oblique projector. Projectors are closely linked to generalized inverses of matrices. For example, for a given matrix A the product PA = AA + is well known as the orthogonal projector on the range (column space) of A, where A+ is the Moore-Penrose inverse of A; which is the unique solution of the following four Penrose equations
8 citations
01 Oct 1985
TL;DR: In this paper, the semigroup of all partial transformations of a vector space into itself was studied in both a topological and a totally ordered setting, and it has been generalized in a different direction by Kim [8] and Magill [10].
Abstract: Let X be a set and the semigroup (under composition) of all total transformations from X into itself. In ([6], Theorem 3) Howie characterised those elements of that can be written as a product of idempotents in different from the identity. We gather from review articles that his work was later extended by Evseev and Podran [3, 4] (and independently for finite X by Sullivan [15]) to the semigroup of all partial transformations of X into itself. Howie's result was generalized in a different direction by Kim [8], and it has also been considered in both a topological and a totally ordered setting (see [11] and [14] for brief summaries of this latter work). In addition, Magill [10] investigated the corresponding idea for endomorphisms of a Boolean ring, while J. A. Erdos [2] resolved the analogous problem for linear transformations of a finite–dimensional vector space.
8 citations
TL;DR: In this article, the authors obtained the general form of bijective order and orthogonality preserving maps on the poset of all n-×-n upper triangular idempotent matrices over an arbitrary field F.
8 citations
TL;DR: In this article, it was shown that the multiplicative Lie-type derivation from R into itself is almost additive under certain assumptions on R, and they proved that D is additive under the assumption that R is a nontrivial idempotent ring.
Abstract: Let R be an alternative ring containing a nontrivial idempotent and D be a multiplicative Lie-type derivation from R into itself. Under certain assumptions on R, we prove that D is almost additive....
8 citations