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

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

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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.

Item Type:
Journal Article
Journal or Publication Title:
K-Theory
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
160249
Deposited By:
Deposited On:
05 Oct 2021 15:00
Refereed?:
Yes
Published?:
Published
Last Modified:
19 Nov 2021 11:59