Structure in Real Banach Spaces. Part II

Alfsen, Erik M.; Effros, Edward G.

doi:10.2307/1970896

Cited by 99 publications

(159 citation statements)

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“…We shall say that a closed subspace X of a Banach space Y has the unique ideal property in Y if there is at most one ideal projection, this is, at most one norm one projection TV on Y* with ker7T = X 1 . From the relation between ideal projections and use, available at https://www.cambridge.org/core/terms.…”

Section: Hahn-banach Extension Operatorsmentioning

confidence: 99%

Ideals of compact operators

Lima¹,

Oja²

2004

J. Aust. Math. Soc.

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We give an example of a Banach space X such that J^(X, X) is not an ideal in J(f(X, X**). We prove that if z* is a weak* denting point in the unit ball of Z* and if X is a closed subspace of a Banach space Y, then the set of norm-preserving extensions HB(x*®z*) c jSf(Z*, Y)* of a functional x*®z* e (Z®X)* is equal to the set HB(x*) ® (z*}. Using this result, we show that if X is an W-ideal in Y and Z is a reflexive Banach space, then Jf(Z, X) is an W-ideal in Jf(Z, Y) whenever JT(Z, X) is an ideal in Jf(Z, Y).We also show that X ( Z , X) is an ideal (respectively, an A/-ideal) in Jf(Z, Y) for all Banach spaces Z whenever X is an ideal (respectively, an M-ideal) in Y and X* has the compact approximation property with conjugate operators.2000 Mathematics subject classification: primary 46B20,46B28, 47L05.

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Section: Hahn-banach Extension Operatorsmentioning

confidence: 99%

Ideals of compact operators

Lima¹,

Oja²

2004

J. Aust. Math. Soc.

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“…A subspace K of a Banach space X is called an M-ideal if the annihila tor K1-is an L-ideal of X* (see [1] for these concepts).…”

Section: Theorem B (77 °° + C)/77°° Is An M-ideal In L^/h"3mentioning

confidence: 99%

Best Approximation in Certain Douglas Algebras

Younis¹

1980

Proceedings of the American Mathematical Society

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“…Then K is just the probability measures on the unit circle F, so that 3^K and 3^Z are both closed. Every point of 3^Z is a split face of Z and so if E C 8^Z, the normclosed convex hull of E (in A(Z)*) is a norm-closed split face ofZ (by the L-ideal theory of [3]). However, take E = 7 U -ry where 7 is a proper arc of V of length > 0.…”

Section: /Gtmentioning

confidence: 99%

Closures of faces of compact convex sets

Roy¹

1975

Annales De L’institut Fourier

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Structure in Real Banach Spaces. Part II

Cited by 99 publications

References 0 publications

Ideals of compact operators

Ideals of compact operators

Best Approximation in Certain Douglas Algebras

Closures of faces of compact convex sets

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