Complete description of derivations on $\tau$-compact operators for type I von Neumann algebras

Abstract: Given a type I von Neumann algebra

M

with a faithful normal semi-finite trace

a u,

let

S_{0} (M, a u)

be the algebra of all

a u

-compact operators affiliated with

M .

We give a complete description of all derivations on the algebra

S_{0} (M, a u) .

In particular, we prove that if

M

is of type I

_{i} n f t y

then every derivation on

S_{0} (M, a u)

is spatial.

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