In this paper, we show the relation between the Schur algebras Sr Λ,Σ(B) and S r′ Λ,Σ(B), where 1 ≤ r ′ < r < ∞. Then we set up the involution operator in these Schur algebras and show that with this involution operator there is only one C∗-algebra among these classes of Banach algebras. Furthermore, we show the equivalence of a condition on the Schur multiplier norm and the existence of C∗-alg...

We study the space of functions ϕ: IN → C such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that ϕ(n) = T n ξ, η. This implies that the matrix (ϕ(i + j)) i,j≥0 is a Schur multiplier of B(ℓ 2) or equivalently is in the space (ℓ 1 ∨ ⊗ ℓ 1) *. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach make...

it is shown that there are exactly seventy-eight 3-generator 2-groups of order $2^{11}$ with trivial schur multiplier. we then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero.