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- ...ence G|last2=Pedersen|authorlink1=Lawrence G. Brown|first2=Gert K|title=C*-algebras of real rank zero|journal=Journal of Functional Analysis|date=July 1991|vol The real rank of a unital C*-algebra ''A'' is the smallest non-negative integer ''n'', denoted RR(''A'' ...5 KB (726 words) - 00:03, 19 August 2023
- ...th>, we have <math>x^\ast\in A</math> and that <math>xy = yx</math>.<ref>{{Cite book |last=Rudin |first=Walter |title=Functional Analysis |publisher=McG ...satisfies <math>\pi(\omega) = \pi(\omega)^*</math> and <math>\pi(\omega) \circ \pi(\omega) = \pi(\omega)</math>) such that ...17 KB (2,933 words) - 23:40, 28 March 2023
Page text matches
- ...escription|Identity valid in special Jordan algebras but not in all Jordan algebras}} ...</ref> which vanishes in all special Jordan algebras but not in all Jordan algebras. What is now known as Glennie's identity first appeared in his 1963 Yale Ph ...2 KB (286 words) - 11:54, 7 June 2024
- {{short description|Metric on the C*-algebras on a fixed Hilbert space}} ...[[Hausdorff distance]] between the [[unit ball]]s of the two C<sup>*</sup>-algebras, under the norm-induced metric on the space of all [[bounded operator]]s on ...2 KB (250 words) - 20:16, 12 August 2019
- ...ality (order theory)|dual endomorphism]], that is, an operation <math>\sim\colon L \to L</math> satisfying ...ere named after [[William of Ockham]] by {{harvtxt|Urquhart|1979}}. Ockham algebras form a [[variety (universal algebra)|variety]]. ...2 KB (253 words) - 01:18, 21 May 2024
- {{Short description|Concept in Lie algebra mathematics}} ...ebra]]s is one of the major achievements of [[Wilhelm Killing]] and [[Élie Cartan]]. ...3 KB (531 words) - 03:00, 27 December 2024
- {{more citations needed|date=November 2014}} ...to a noncommutative setting by studying those ideas on general von Neumann algebras. ...3 KB (468 words) - 18:55, 23 January 2022
- ...ot the former, topological, condition, and use only the latter, algebraic, condition. ...[self-adjoint]] [[idempotent element (ring theory)|idempotent element]]. A C*-algebra ''A'' is an AW*-algebra if for every subset ''S'' of ''A'', the le ...4 KB (632 words) - 12:23, 5 February 2025
- ...r reductive Lie algebras, the Cartan subalgebra is required to contain the center. ...jugate; thus split Lie algebras are of most interest for non-algebraically closed fields. ...5 KB (790 words) - 19:44, 26 January 2024
- ...ons of C*-algebras. It implies that, for irreducible representations of C*-algebras, the only non-zero linear invariant subspace is the whole space. ...ucibly'' when <math>\{0\}</math> and <math>\mathcal{H}</math> are the only closed stable subspaces under <math>\mathcal{F}</math>. The family <math>\mat ...3 KB (374 words) - 17:50, 18 July 2024
- ...or]] category. Lie conformal algebras are very closely related to [[vertex algebras]] and have many applications in other areas of algebra and integrable syste ==Definition and relation to Lie algebras== ...3 KB (449 words) - 19:11, 22 July 2022
- ...tragraph, and similarly, every infinite graph giving an Exel-Laca algebras can also be encoded as an ultragraph. ...h> of nonempty subsets of the vertex set. A directed graph is the special case of an ultragraph in which the range of each edge is a singleton, and ult ...6 KB (976 words) - 09:20, 30 August 2023
- ...of positivity. Thus it links [[operator algebra]]ic and [[Convex function|convex]] [[Order theory|order theoretic]] views on state spaces of physical s ...both <math>a</math> and <math>-a</math> are in the closure <math>\overline{C}</math>. ...3 KB (428 words) - 22:50, 13 April 2021
- {{More citations needed|date=August 2020}} {{DISPLAYTITLE:Exact C*-algebra}} ...2 KB (287 words) - 13:23, 23 August 2020
- In [[abstract algebra]], a '''unital map''' on a [[C*-algebra]] is a map <math>\phi</math> which preserves the identity element: This condition appears often in the context of [[completely positive map]]s, especially when they represent [[quantum operatio ...1,013 bytes (150 words) - 15:10, 21 April 2022
- ...an [[operad]]. It is a generalization of an [[associative algebra]] over a commutative ring ''R'', with an operad replacing ''R''. ...'' (say, a [[symmetric sequence]] in a [[symmetric monoidal ∞-category]] ''C''), an '''algebra over an operad''', or '''''O''-algebra''' for short, is, ...2 KB (235 words) - 17:53, 23 April 2024
- ...mmutant-associative algebra''' is a [[Algebra over a field#Non-associative algebras|nonassociative algebra over a field]] whose [[product (mathematics)|multipl where [''A'', ''B''] = ''AB'' − ''BA'' is the [[commutator]] of ''A'' and ''B'' and ...3 KB (364 words) - 15:39, 20 March 2023
- ...ence G|last2=Pedersen|authorlink1=Lawrence G. Brown|first2=Gert K|title=C*-algebras of real rank zero|journal=Journal of Functional Analysis|date=July 1991|vol The real rank of a unital C*-algebra ''A'' is the smallest non-negative integer ''n'', denoted RR(''A'' ...5 KB (726 words) - 00:03, 19 August 2023
- ...r '''dual Leibniz algebra''' is a [[module (mathematics)|module]] over a [[commutative ring]] with a [[bilinear map|bilinear]] product satisfying the de :<math>(a \circ b) \circ c = a \circ (b \circ c) + a \circ (c \circ b).</math> ...3 KB (375 words) - 23:09, 10 July 2022
- ...y of C*-algebras which was proved by [[Gilles Pisier]] in 1978 affirming a conjecture of [[John Ringrose]]. It is an extension of the [[Grothendieck ine ...d, linear mapping of one C*-algebra <math>\mathfrak{A}</math> into another C*-algebra <math>\mathfrak{B}</math>, then ...2 KB (235 words) - 09:24, 18 August 2023
- ...a [[Noncommutative geometry|noncommutative space]] in the sense of [[Alain Connes]]. ...re-integrable function]]s on the [[unit circle]] <math>S^1 \subset \mathbb{C}</math>, generated by two [[unitary operator|unitary]] operators <math>U, V ...5 KB (736 words) - 23:18, 10 June 2024
- ...baric algebras''' (also called '''weighted algebra'''). The study of these algebras was started by {{harvs|txt|authorlink=Ivor Malcolm Haddon Etherington|last= ...orresponding to the genetically different [[gamete]]s, and the [[structure constants]] of the algebra encode the probabilities of producing offspring of ...8 KB (1,160 words) - 09:53, 10 February 2025