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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces. / Laustsen, Niels Jakob.
In: K-Theory, Vol. 23, No. 2, 30.06.2001, p. 115-127.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Laustsen, NJ 2001, 'K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces', K-Theory, vol. 23, no. 2, pp. 115-127. https://doi.org/10.1023/A:1017573608843

APA

Laustsen, N. J. (2001). K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces. K-Theory, 23(2), 115-127. https://doi.org/10.1023/A:1017573608843

Vancouver

Laustsen NJ. K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces. K-Theory. 2001 Jun 30;23(2):115-127. doi: 10.1023/A:1017573608843

Author

Laustsen, Niels Jakob. / K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces. In: K-Theory. 2001 ; Vol. 23, No. 2. pp. 115-127.

Bibtex

@article{aa857f83e0ea42da86dc0de5abdaf0ea,
title = "K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces",
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.",
keywords = "Banach algebra, James spaces, Operators on a Banach space",
author = "Laustsen, {Niels Jakob}",
year = "2001",
month = jun,
day = "30",
doi = "10.1023/A:1017573608843",
language = "English",
volume = "23",
pages = "115--127",
journal = "K-Theory",
issn = "0920-3036",
publisher = "Kluwer Academic Publishers",
number = "2",

}

RIS

TY - JOUR

T1 - K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces

AU - Laustsen, Niels Jakob

PY - 2001/6/30

Y1 - 2001/6/30

N2 - 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.

AB - 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.

KW - Banach algebra

KW - James spaces

KW - Operators on a Banach space

U2 - 10.1023/A:1017573608843

DO - 10.1023/A:1017573608843

M3 - Journal article

AN - SCOPUS:0442310773

VL - 23

SP - 115

EP - 127

JO - K-Theory

JF - K-Theory

SN - 0920-3036

IS - 2

ER -