Naslov
The cb-norm approximation of generalized skew derivations by elementary operators

Autori
Gogić, Ilja

Izvornik
Linear and multilinear algebra (0308-1087) 69 (2021), 8; 1543-1556

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
elementary operator ; generalized skew derivation ; epimorphism ; prime C*-algebra

Sažetak
Let A be a ring and σ:A→A a ring endomorphism. A generalized skew (or σ-)derivation of A is an additive map d:A→A for which there exists a map δ:A→A such that d(xy)=δ(x)y+σ(x)d(y) for all x, y∈A. If A is a prime C∗-algebra and σ is surjective, we determine the structure of generalized σ-derivations of A that belong to the cb-norm closure of elementary operators Eℓ(A) on A ; all such maps are of the form d(x)=bx+axc for suitable elements a, b, c of the multiplier algebra M(A). As a consequence, if an epimorphism σ:A→A lies in the cb-norm closure of Eℓ(A), then σ must be an inner automorphism. We also show that these results cannot be extended even to relatively well-behaved non-prime C∗-algebras like C(X, M2).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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