Local Triple Derivations on Real C $$^*$$ ∗ -Algebras and JB $$^*$$ ∗ -Triples

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Automatic Continuity of Higher Derivations on JB*-Algebras

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.

Little Grothendieck’s theorem for real JB*-triples

We prove that given a real JB*-triple E, and a real Hilbert space H , then the set of those bounded linear operators T from E toH , such that there exists a norm one functionalφ ∈ E∗ and corresponding pre-Hilbertian semi-norm ‖.‖φ on E such that ‖T (x)‖ ≤ 4 √ 2‖T‖ ‖x‖φ for all x ∈ E, is norm dense in the set of all bounded linear operators from E toH . As a tool for the above result, we show th...

Triple Derivations on Von Neumann Algebras

It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its pr...