Elementary operators on prime C*-algebras II

S - Numbers of Elementary Operators on C ∗ - Algebras

We study the s-numbers of elementary operators acting on C∗algebras. The main results are the following: If τ is any tensor norm andA,B ∈ B(H) are such that the sequences s(A), s(B) of their singular numbers belong to a stable Calkin space i then the sequence of approximation numbers ofA⊗τB belongs to i. If A is a C∗-algebra, i is a stable Calkin space, s is an s-number function, and ai, bi ∈ A...

Prime Higher Derivations on Algebras

Spectrally Bounded Operators on Simple C∗-algebras

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ M r(x) for all x ∈ E, where r( · ) denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple C∗-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.

On a functional equation for symmetric linear operators on $C^{*}$ algebras

‎Let $A$ be a $C^{*}$ algebra‎, ‎$T‎: ‎Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $‎. ‎We prove that under each of the following conditions‎, ‎$T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: ‎‎ ‎i) $A$ is a simple $C^{*}$-algebra‎. ‎ii) $A$ is unital with trivial center and has a faithful trace such ...

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.