Citation:
A S. On the norm of elementary operatorsin standard operator algebras. Acta Sci. Math. (Szeged). 2004;70 :229-236.
 | ameur_acta_2004.pdf | 96 KB |
Abstract:
Let A be a complex normed algebra. For A,B ∈ A, define a basicelementary operator MA,B : A → A by MA,B(X) = AXB.
Given a standard operator algebra A acting on a complex normed space
and A,B ∈ A we have:
(i) The lower estimate kMA,B +MB,Ak ≥ 2(√2 − 1)kAkkBk holds.
(ii) The lower estimate kMA,B +MB,Ak ≥ kAkkBk holds if
inf
∈C kA + Bk = kAk or inf
∈C kB + Ak = kBk.
(iii) The equality kMA,B +MB,Ak = 2kAkkBk holds if
kA + Bk = kAk + kBk for some unit scalar .
These results extend analogous estimates established earlier for standard
operator subalgebras of Hilbert space operators.