Geometry of the Unit Ball and Representation Theory for Operator Algebras
نویسندگان
چکیده
We investigate the relationship between the facial structure of the unit ball of an operator algebra A and its algebraic structure, including the hereditary subalgebras and the socle of A. Many questions about the facial structure of A are studied with the aid of representation theory. For that purpose we establish the existence of reduced atomic type representations for certain nonselfadjoint operator algebras. Our results are applicable to C∗-algebras, strongly maximal TAF algebras, free semigroup algebras and various semicrossed products.
منابع مشابه
Commutative C ∗ - algebras of Toeplitz operators on the unit ball , II . Geometry of the level sets of symbols
In the first part [16] of this work, we described the commutative C∗algebras generated by Toeplitz operators on the unit ball B whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of B. Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of the unit disk (see [3]) admits a natural generaliza...
متن کاملON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY
Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...
متن کاملParabolic starlike mappings of the unit ball $B^n$
Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...
متن کاملPositive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras
In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.
متن کاملQuantum Mechanics and Operator algebras on the Hilbert ball
We study Kähler functions on the Hilbert ball and and the algebra of Kähler functions. We introduce quantum mechanics and operator algebras on the Hilbert ball by using the theory of geometrical quantum mechanics.
متن کامل