Laustsen, Niels Jakob
(2001)
*K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces.*
K-Theory, 23 (2).
pp. 115-127.
ISSN 0920-3036

## Abstract

We prove that the K-groups of the Banach algebra script B sign(script J signp) of bounded, linear operators on the pth James space script J signp, where 1 < p < ∞, are given by K0(script B sign(script J signp)) ≅ ℤ and K1(script B sign(script J signp)) = {0}. Moreover, for each Banach space script X sign and each non-zero, closed ideal script I sign in script B sign(script X sign) contained in the ideal of inessential operators, we show that K0(script I sign) ≅ ℤ and K1(script I sign) = {0}. This enables us to calculate the K-groups of script B sign(script X sign) for each Banach space script X sign which is a direct sum of finitely many James spaces and ℓp-spaces.