On the Distance between an Operator and an Ideal
Nicolae Tiţa · Birkhäuser Basel eBooks · 2004
Let L ( X ) be the normed algebra of all bounded linear operators T : X → X , where X is a normed space, and let I be an operator ideal, so that I ( X ) is a two-sided ideal in L ( X ). If X is a tensor product of normed spaces, endowed with a tensor norm, an estimation is given for the distance of a tensor product operator T Є L ( X ) to I ( X ) and it is applied to the study of the quasi-nilpotency of tensor product operators modulo I ( X ).