Naslov
Two-sided multiplications and phantom line bundles

Autori
Gogić, Ilja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
XIX Geometrical Seminar

Mjesto i datum
Zlatibor, Srbija, 28.08.2016. - 04.09.2016

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
C*-algebra ; Homogeneous ; Two-sided multiplication ; Elementary operator ; Complex line bundle

Sažetak
Two-sided multiplications M_{; ; a, b}; ; :x→axb on C*- algebras A, where a and b are elements of A, are usually considered as basic building blocks for more general types of operators on A, as their finite sums (i.e. elementary operators) comprise both inner derivations and inner automorphisms. It is therefore natural to ask which operators φ:A→A can be obtained as operator-norm limits of TMs. Let us denote by TM(A) the set of all TMs on A. We first show that TM(A) is closed in the operator norm for all prime C*-algebras A. On the other hand, if A\cong Γ_0(E) is an n-homogeneous C*-algebra, where E is the canonical M_n-bundle over the primitive spectrum X of A, we show that TM(A) fails to be closed in the operator norm if and only if there exists a σ-compact open subset U of X and a phantom complex line subbundle L of E over U (i.e. L is not globally trivial, but is trivial on all compact subsets of U). This phenomenon occurs whenever A is non-commutative and X is a CW-complex (or a topological manifold) of dimension 3≤d<∞. This is a joint work with Richard M. Timoney (Trinity College Dublin).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA