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.     

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})} .     

Burnside algebra of a finite inverse semigroup

The Burnside algebra for a finite inverse semigroup over a field is considered (the analog of the Grothendieck algebra). The conditions for the algebra to be Frobenius are investigated. It is shown that, if all the subgroups in the semigroup are commutative, then its Burnside algebra is Frobenius if and only if the order of any maximal subgroup is not divisible by the square of the field characteristic.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 41–52, 1974.     

A simple separable C*-algebra not isomorphic to its opposite algebra

We give an example of a simple separable C*-algebra that is not isomorphic to its opposite algebra. Our example is nonnuclear and stably finite, has real rank zero and stable rank one, and has a unique tracial state. It has trivial , and its -group is order isomorphic to a countable subgroup of .

     

The maximal C*-algebra of quotients as an operator bimodule

In this article we extend the work on strongly p-embedded subgroups in Parker and Stroth (Strongly p-embedded subgroups, arxiv:0901.0805) to include the Lie type groups of rank 2.     

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.     

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 ${\mathcal{A}}$ .     

Center of the semigroup algebra of a finite inverse semigroup over the field of complex numbers

In the semigroup algebra A of a finite inverse semigroup S over the field of complex numbers to an indempotent e there is assigned the sum (e)=e+(–1)^Ke_L1e_iK, where e_i,...,e_m are maximal preidempotents of the idempotent e, and the summation goes over all nonempty subsets {i₁,...,i_k} of the set {1,...m} Then for any class K of conjugate group elements of the semigroup S the element K=a·(a^–1a) (the summation goes over all ag) is a central element of the algebra A, and the set {K} of all possible such elements is a basis for the center of the algebra A.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 154–158, 1978.     

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.     

On module cohomology of the Fourier algebra of an inverse semigroup

Semigroup Forum - For an inverse semigroup S with the set of idempotents E, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character...     

C~* -代数上完全正映射的刻画

本文给出C* -代数之间完全正映射的刻画,证明:如果A,B是有单位元的C*-代数,则映射Φ:A→B为完全正映射当且仅当存在保单位*-同态πA:A→B(K)、等距* -同态πB:B→B(H)及有界线性算子V:H→K,使得πB(Φ(1))=V*V 且■a∈A,都有πB(Φ(a))=V*π(a)V.作为推论,得到著名的Stinespring膨胀定理.     

Module operator virtual diagonals on the Fourier algebra of an inverse semigroup

For an amenable inverse semigroup S with the set of idempotents E and a minimal idempotent, we explicitly construct a contractive and positive module operator virtual diagonal on the Fourier algebra A(S), as a completely contractive Banach algebra and operator module over \(\ell ^1(E)\). This generalizes a well known result of Zhong-Jin Ruan on operator amenability of the Fourier algebra of a (discrete) group Ruan (Am J Math 117:1449–1474, 1995).     

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.