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...ons of C*-algebras. It implies that, for irreducible representations of C*-algebras, the only non-zero linear invariant subspace is the whole space. ...<math>Ax_j = y_j</math>. If <math>Bx_j = y_j</math> for some self-adjoint operator <math>B</math>, then <math>A</math> can be chosen to be self-adjoint. ...

...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 ...

(The <math>E_i</math> are the [[Kraus operator]]s associated with <math>\phi</math>). In this case, the unital condition ...www.worldcat.org/oclc/228110971|title=Completely bounded maps and operator algebras|date=2002|publisher=Cambridge University Press|isbn=0-511-06103-X|location= ...

{{short description|Metric on the C*-algebras on a fixed Hilbert space}} ...sup>-algebras, under the norm-induced metric on the space of all [[bounded operator]]s on that Hilbert space. ...

{{Short description|Mathematical operator}} ...ntial operator]] defined by<ref>{{MathWorld |id=ThetaOperator |title=Theta Operator |access-date=2013-02-16}}</ref><ref>{{cite book|last=Weisstein|first=Eric W ...

...Similarly, a [[nonassociative algebra]] is flexible if its multiplication operator is flexible. ...they satisfy the flexible identity.<ref>Richard D. Schafer (1954) “On the algebras formed by the Cayley-Dickson process”, [[American Journal of Mathematics]] ...

...ed with a binary operator, the commutator <math>[x,y]</math> and a ternary operator, the associator <math>[x,y,z]</math> that satisfy a particular relationship ...t[x,y\right]</math> is bilinear and [[anticommutative]]; and the trilinear operator <math>\left(x,y,z\right)\mapsto\left[x,y,z\right]</math> satisfies the ''Ak ...

{{Short description|Theorem of operator algebra}} ...eal Jordan algebras]] and so-called domains of positivity. Thus it links [[operator algebra]]ic and [[Convex function|convex]] [[Order theory|order theoretic]] ...

...to a noncommutative setting by studying those ideas on general von Neumann algebras. ...ebras with a faithful normal tracial state, for example finite von Neumann algebras, the notion of conditional expectation is especially useful. ...

...are determined to a large extent by their projections. The idea behind AW*-algebras is to forgot the former, topological, condition, and use only the latter, a Hence an AW*-algebra is a C*-algebras that is at the same time a [[Baer *-ring]]. ...

...s]], '''Pisier–Ringrose inequality''' is an inequality in the theory of C*-algebras which was proved by [[Gilles Pisier]] in 1978 affirming a conjecture of [[J | title = Grothendieck's theorem for noncommutative C^∗-algebras, with an appendix on Grothendieck's constants ...

...st = Robert S. |author2=Victor A. Belfi | title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems | publisher = Marcel Dekker | location = New ...=B. |author2=H. A. Dye |year=1966|title=A Note on Unitary Operators in C*-Algebras |journal=Duke Mathematical Journal |volume=33 |pages=413–416 |doi=10.1215/S ...

...is the case where <math>\mathcal{A}</math> is a [[Banach algebra#Banach *-algebras|complete normed *-algebra]]. This algebra satisfies the C*-identity (<math> * [[Unitary operator]] ...

...commutative C*-algebras which generalize the [[C*-algebra#Commutative C.2A-algebras|algebra of continuous functions]] on the [[Torus|2-torus]]. Many topologica ...t circle]] <math>S^1 \subset \mathbb{C}</math>, generated by two [[unitary operator|unitary]] operators <math>U, V</math> defined as<blockquote><math>\begin{al ...

...as an ultragraph, and similarly, every infinite graph giving an Exel-Laca algebras can also be encoded as an ultragraph. === Ultragraph algebras === ...

...eries]]. Chiral algebras on curves are essentially [[vertex algebra#vertex operator algebra|conformal vertex algebra]]s. ...k |last1=Ben-Zvi |first1=David |last2=Frenkel |first2=Edward |title=Vertex algebras and algebraic curves |date=2004 |publisher=American Mathematical Society |l ...

In mathematics, a '''weak trace class''' operator is a [[compact operator]] on a [[separable space|separable]] [[Hilbert space]] ''H'' with [[singula ...has fundamentally different properties. The usual [[trace class#Definition|operator trace]] on the trace-class operators does not extend to the weak trace clas ...

...th>-[[invariant subspace]]s.<ref>{{cite arXiv|title=Central Simple Poisson Algebras|author1=Yucai Su|author2=Xiaoping Xu|eprint=math/0011086v1|year=2000}}</ref ...5629 }}</ref> If <math>V</math> is also a [[Hilbert space]], sometimes an operator is called locally finite when the sum of the <math>\{ V_i\vert i\in I\}</ma ...

...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 ...unori|last2=Osaka|first2=Hiroyuki|title=Real Rank of Tensor Products of C*-algebras|journal=Proceedings of the American Mathematical Society|date=July 1995|vol ...

...url=http://web.math.ku.dk/~rordam/}}</ref> specializing in the theory of [[operator algebra]]s and its applications. ...2010 to 2016. He was a plenary speaker at the [[International Workshop on Operator Theory and its Applications]] (IWOTA) in 2018 in Shanghai.<ref name=CV/> ...