Let A be a C*-algebra with state space S. The representation := on the Hilbert space is known as the universal representation of A. As the universal representation is faithful, A is *-isomorphic …

Algebra is the branch of mathematics that studies algebraic structures and the operations they use. [1] An algebraic structure is a non-empty set of mathematical objects, such as the …

In mathematics, the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A.

Een C*-algebra is een Banach-algebra uitgerust met een involutie die voldoet aan de normgelijkheid. {\displaystyle \forall a\in {\mathcal {A}}:\left\|aa^ {*}\right\|=\left\|a\right\|^ {2}.} In …

Jan 31, 2025 · A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies (x^*)^* = x (1) x^*y^* = (yx)^* (2) x^*+y^* = (x+y)^* (3) (cx)^* = c^_x^*, (4) where c^_ is …

An algebra with an involution is a *-algebra. Definition 1. A Banach *-algebra A is called a C*-algebra if kx ⇤xk = kxk2,x2A. Proposition 1. Let A be a C*-algebra. 1. kx ⇤ k = kxk; 2. If A …

C∗-algebras (pronounced "C-star") are subjects of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra A of continuous linear operators on a …

Apr 20, 2012 · Any $\Cstar$-algebra is isometrically and symmetrically isomorphic to a $\Cstar$-subalgebra of some $\Cstar$-algebra of the form $L (H)$.

The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra.. In mathematics, more specifically algebra, abstract algebra or modern algebra is the …

These include C*-algebras, von Neumann algebras, and AW*-algebras. C*-algebras can be easily characterized abstractly by a condition relating the norm, involution and multiplication. Such …

A matematikában a C*-algebra olyan Banach-algebra, mely el van látva egy, az adjungálás (konjugált transzponálás) tulajdonságaival rendelkező involúcióval. A C*-algebrákat először a …

Nov 23, 2017 · The C$^*$-algebra generated by a unitary $u$ has two relations, namely $u^*u=uu^*=I$, so it is not free. Given any free group, you can certainly generate a C$^*$ …

C∗-algebras are historically linked to the development of quantum mechanics through the groundbreaking work of John von Neumann (1903–1957) in the late 1920s, and since the …

The fundamental theorem of algebra, also called d'Alembert's theorem [1] or the d'Alembert–Gauss theorem, [2] states that every non-constant single-variable polynomial with …

One checks that m(a)b = m(ab) 8a; b 2 A and m; m are bounded. M(A) becomes a unital C -algebra with respect to. If A C M then 9 : M ! M(A); (m)(a) := ma, which is faithful if A C M …

C (pronounced / ˈ s iː / – like the letter c) [6] is a general-purpose programming language.It was created in the 1970s by Dennis Ritchie and remains very widely used and influential. By …

In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular …

数学における C*-環（シースターかん、英: C*-algebra ）とは複素数体上の完備なノルム環で複素共役に類似の作用をもつものであり、フォン・ノイマン環と並ぶ作用素環論の主要な研究対 …