Prime ideals in the C*-algebra of a nilpotent group

We say that a locally compact groupG hasT ₁ primitive ideal space if the groupC ^*-algebra,C ^*(G), has the property that every primitive ideal (i.e. kernel of an irreducible representation) is closed in the hull-kernel topology on the space of primitive ideals ofC ^*(G), denoted by PrimG. This means of course that every primitive ideal inC ^*(G) is maximal. Long agoDixmier proved that every connected nilpotent Lie group hasT ₁ primitive ideal space. More recentlyPoguntke showed that discrete nilpotent groups haveT ₁ primitive ideal space and a few month agoCarey andMoran proved the same property for second countable locally compact groups having a compactly generated open normal subgroup. In this note we combine the methods used in [3] with some ideas in [9] and show that for nilpotent locally compact groupsG, having a compactly generated open normal subgroup, closed prime ideals inC ^*(G) are always maximal which implies of course that PrimG isT ₁.     

Fuzzy quasi C*-algebra

At the present paper, the new concepts of fuzzy quasi norm, fuzzy Banach space, fuzzy quasi continuity and fuzzy quasi boundedness is introduced. Furthermore, we define the fuzzy quasi operator norm and also it is shown that the set all of fuzzy quasi bounded operator from X to Y is fuzzy quasi Banach space. Finally, we have introduced and investigated some notions and some results on *-algebra theory.     

Asymptotic representations of the reduced C*-algebra of a free group: an example

We give an example of a non-trivial asymptotic representationof the reduced C*-algebra of a free group. This example allowsus to evaluate the asymptotic tensor C*-norm of some elementsin tensor product C*-algebras and to show semi-invertibilityof the non-invertible extension of C*_r(₂) considered by Haagerupand Thorbjørnsen.     

On the homotopy type of the regular group of a realW *-algebra

In this paper we determine the homotopy groups of the group of invertible elements of a purely realW ^*-algebra of typeII ₁. It turns out that the homotopy groups are periodic with period 4.     

Alternating group covers of the affine line

For an odd prime p t= 2 mod 3, we prove Abhyankar’s Inertia Conjecture for the alternating group A _p+2, by showing that every possible inertia group occurs for a (wildly ramified) A _p+2-Galois cover of the projective k-line branched only at infinity where k is an algebraically closed field of characteristic p > 0. More generally, when 2 ≤ s < p and gcd(p−1, s+1) = 1, we prove that all but finitely many rational numbers which satisfy the obvious necessary conditions occur as the upper jump in the filtration of higher ramification groups of an A _p+s -Galois cover of the projective line branched only at infinity.     

The multiplier algebra of a nuclear quasidiagonal C*-algebra

If is a unital separable simple nuclear quasidiagonal C*-algebra,then ( ) has the AF-property in the strict topology; that is,there is a unital AF-subalgebra ( ) such that is strictlydense in ( ). We also give a multiplier algebra characterizationof nuclearity and quasidiagonality for a unital separable simpleC*-algebra.     

On the Borel envelopingC *-algebra of aC *-algebra

L’auteur introduit et étudie laC ^*-algèbre enveloppante borelienne d’uneC ^*-algebre quelconque. On montre que le foncteur defini est exact et que la représentation atomique est fidèle. Si laC ^*-algèbre initiale est commutative, la constructian fournit laC ^*-algèbre des fonctions complexes bornées boreliennes sur le spectre de l’algèbre donnée.     

A properly discontinuous free group of affine transformations

In this paper we prove that a fully irreducible outer automorphism relative to a non-exceptional free factor system acts loxodromically on the relative free factor complex as defined in Handel and Mosher (Relative free splitting and relative free factor complexes I: hyperbolicity, 2014. arXiv:1407.3508v1). We also prove a north-south dynamic result for the action of such outer automorphisms on the closure of relative outer space.     

The model theory of modules of a C*-algebra

We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show that there is an homeomorphism between the space of types of norm less than 1 in this model companion, and the space of quasistates of the C*-algebra ${\mathcal{A}}$ .     

The C*-algebra of the N-dimensional harmonic oscillator

In this paper we study the Fredholm thoery of a C*-algebraOl of o-order pseudo-differential operators on L²(ⁿ). IfK denotes the ideal of all compact operators of L², the algebraOl will be generated by (i) the idealK, (ii) a function algebra CS(ⁿ) and (iii) by the bounded operators x_j, D_j, j=1,...,n, = H^–1/2, H=1+¦x¦²–. We show thatOl/K is a commutative C*-algebra with identity and obtain its Gelfany space M. This provides Fredholm criterion and index formula for a graded algebra of partial differential operators including all oeprators with polynomial coefficients. We also give Fredholm criterion and index formula for systems of such operators.     

Ideals of a C *-algebra generated by an operator algebra

In this paper, we consider ideals of a C ^*-algebra C^*(B){C^*(\mathcal{B})} generated by an operator algebra B{\mathcal{B}} . A closed ideal J í C^*(B){J\subseteq C^*(\mathcal{B})} is called a K-boundary ideal if the restriction of the quotient map on B{\mathcal{B}} has a completely bounded inverse with cb-norm equal to K ⁻¹. For K = 1 one gets the notion of boundary ideals introduced by Arveson. We study properties of the K-boundary ideals and characterize them in the case when operator algebra λ-norms itself. Several reformulations of the Kadison similarity problem are given. In particular, the affirmative answer to this problem is equivalent to the statement that every bounded homomorphism from C^*(B){C^*(\mathcal{B})} onto B{\mathcal{B}} which is a projection on B{\mathcal{B}} is completely bounded. Moreover, we prove that Kadison’s similarity problem is decided on one particular C ^*-algebra which is a completion of the *-double of M₂(\mathbbC){M_2(\mathbb{C})} .     

On the bounded part of a Hilbert module over a locally C *-algebra

We will show that the bounded part of the locally C^*-algebra of all adjointable operators on the Hilbert A-module E is isomorphic to the C^*-algebra L _b(A)(b(E)) of all adjointable operators on the Hilbert b(A)-module b(E). This revised version was published online in June 2006 with corrections to the Cover Date.     

On the spectrum of the C*-algebra of fourier multipliers in a cone

We describe the spectrum of the C^*-algebra generated by the Fourier multipliers (singular integral operators) on the space L₂ with a polynomial weight in an acute-angled convex cone of the space ⁿ. Bibliography: 12 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 61–82.     

某些C*-代数上的2-局部映射

讨论了单C*代数上的2-局部等距的线性;在证明某些C*代数上的2-局部自同构是线性的同时,根据C*代数的K-理论,给出了满足此结果的C*代数例子.