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K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>30/06/2001
<mark>Journal</mark>K-Theory
Issue number2
Volume23
Number of pages13
Pages (from-to)115-127
Publication StatusPublished
<mark>Original language</mark>English

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.