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Operator algebra

About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.


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Journal Article
TL;DR: The spatial operator algebra framework for the dynamics of general multibody systems is described in this article, where the use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multi-body systems in a concise and systematic way.
Abstract: The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

100 citations

Journal ArticleDOI
01 Mar 1990
TL;DR: In this article, it was shown that the Cuntz-Krieger algebras have the FS property and that the set of self-adjoint elements with finite spectrum is norm dense.
Abstract: An alternative proof is given for the fact ([ 13]) that a purely infinite, simple C *-algebra has the FS property: the set of self-adjoint elements with finite spectrum is norm dense in the set of all self-adjoint elements. In particular, the Cuntz algebras O, (2 < n < +oo) and the Cuntz-Krieger algebras 0A if A is an irreducible matrix, have the FS property. This answers a question raised in [2, 2.10] concerning the structure of projections in the Cuntz algebras. Moreover, many corona algebras and multiplier algebras have the FS property. A C -algebra A is said to be purely infinite if (xAx) contains an infinite projection for every nonzero positive element x in A ([7, 12]). The author recently proved ([13]) that purely infinite, simple C*-algebras have the FS property; namely, the set of self-adjoint elements with finite spectrum is norm dense in the set of all self-adjoint elements. Actually, many interesting C*-algebras have the FS property. For example, the Bunce-Deddens algebras have FS ([1, 3]); many corona algebras and multiplier algebras have FS ([5, 13]); certain irrational rotation algebras have FS ([6]). Certainly, all AF algebras, von Neumann algebras, and A W* algebras have FS. In this short note, we provide another proof for the fact that purely infinite, simple C*-algebras have the FS property. The algebras ON (2 < n < +00) and OA, if A is an irreducible matrix, are purely infinite and simple ([7, 8, 9]), and many corona algebras are purely infinite and simple ([12, 13]). Hence, these C*-algebras have the FS property. In particular, this answers a question of B. Blackadar raised in [2, 2.10] concerning the projection structure of the Cuntz algebras. 1. Theorem. If A is a purely infinite, simple C* -algebra, then A has the FS property, and hence RR(A) = 0. Proof. To prove the conclusion, by [2, 2.7; 10], it is equivalent to prove that every hereditary C*-subalgebra of A has an approximate identity consisting of Received by the editors April 17, 1989 and, in revised form, September 5, 1989; the results in this paper were presented at the 17th Annual Canadian Symposium on Operator Algebras and Operator Theory, University of Toronto, May 22-26, 1989. 1980 Mathematics Subject Classification (1985 Revision). Primary 46L05.

100 citations

Book
01 Jan 1985
TL;DR: In this article, the authors consider the following types of multiplications and onto-isomorphisms: 1. Perturbation of multiplication and onto isomorphisms; 2. Into-isomorphic multiplications; 3. Isometries in semisimple, commutative Banach algebras; 4. Stability.
Abstract: Preliminaries.- I. Perturbations of multiplications and onto-isomorphisms.- II. Into-isomorphisms.- III. Isometries in semisimple, commutative Banach algebras.- IV. Perturbations of operator algebras.- V. Stability.

99 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a systematic study of matrix product operators and show how this relates entanglement properties of projected entangled-pair states to the formalism of fusion tensor categories.

99 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that any theory of charged fermions coupled to an abelian gauge field with Chern-Simons term in the action is equivalent to some local theory of (locally gauge invariant) bosonic fields.

99 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202337
202277
2021125
2020141
2019173
2018169