Abstract: Suppose p: C(K) L(X)  is a bounded unital algebra homomorphism where K is a compact 

Hausdorff space, C(K) is the complex valued continuous functions on K and L(X) is the bounded linear 

operators on the Banach space X. Suppose, furthermore, X has a cyclic vector. In this work we show 

that a unital transitive subalgebra of L(X⁽ⁿ⁾) whose weak operator closure contains p(C(K))ⁿ is dense in 

L(X⁽ⁿ⁾) with respect to the weak operator topology. This generalizes similar results of W.B. Arveson [1], 

R.G. Douglas and C.Pearcy [5] on Hilbert spaces and a result of P.Rosenthal and A.R. Sourour [15] on 

cyclic Banach spaces. 

Key words: Transitive algebras of operators, invariant subspaces, n-normal operators, matrix operators.