Strict u-ideals in Banach spaces

Lima, Vegard; Lima, Åsvald

doi:10.4064/sm195-3-6

Cited by 7 publications

(6 citation statements)

References 27 publications

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“…By Theorem 2.4 in [LL09] X is a strict u-ideal in Z. This is true for any y ∈ Y and so, by Proposition 2.1 in [LL09], X is a strict u-ideal in Y .…”

Section: Let (X *mentioning

confidence: 83%

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Almost Isometric Ideals in Banach Spaces

Abrahamsen¹,

Lima

Nygaard³

2013

Glasgow Math. J.

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A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they inherit diameter 2 properties and the Daugavet property. Lindenstrauss spaces are known to be the class of Banach spaces that are ideals in every superspace; we show that being an almost isometric ideal in every superspace characterizes the class of Gurariy spaces.

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“…By Theorem 2.4 in [LL09] X is a strict u-ideal in Z. This is true for any y ∈ Y and so, by Proposition 2.1 in [LL09], X is a strict u-ideal in Y .…”

Section: Let (X *mentioning

confidence: 83%

“…This is well-studied in the recent literature (see e.g. [Rao01] or [LL09]); these ideals are called strict ideals.…”

Section: Let (X *mentioning

confidence: 99%

Almost Isometric Ideals in Banach Spaces

Abrahamsen¹,

Lima

Nygaard³

2013

Glasgow Math. J.

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“…We know that strictly u-embedded spaces have the unique extension property (UEP), i.e., E (X * * , X * * ) = {I X * * } (see [12,Theorem 2.3…”

Section: Unique Extension and Strict U-idealsmentioning

confidence: 99%

“…In [12] Lima and Lima characterized when a Banach space X is strictly uembedded both in terms of the canonical projection π X * * * on X * * * onto X * and in terms of subspaces of X. (Note that π X * * * = k X * (k X ) * where k X is the canonical embedding of X into X * * defined by k X x(x * ) = x * (x).)…”

Section: Strict U-ideals In the Space Of Baire-one Functionsmentioning

confidence: 99%

Strict U-Ideals and U-Summands in Banach Spaces

Abrahamsen¹

2014

MATH. SCAND.

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For a strict u-ideal $X$ in a Banach space $Y$ we show that the set of points in the dual unit ball $B_{X^{\ast}}$, strongly exposed by points in the range $\it TY$ of the unconditional extension operator $T$ from $Y$ into the bidual $X^{\ast\ast}$ of $X$, is contained in the weak$^{\ast}$ denting points in $B_{X^{\ast}}$. We also prove that a u-embedded space is a u-summand if and only if it contains no copy of $c_0$ if and only if it is weakly sequentially complete.

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“…Let us now relate the notion of an ai-ideal to the well established notion of a strict ideal (see e.g. [GKS93], [LL09], [Rao01], and [Abr14]). We say that X is a strict ideal in Y if X is an ideal in Y with an associated ϕ ∈ H B(X, Y ) whose range is 1-norming for Y , i.e.…”

Section: Introductionmentioning

confidence: 99%

EMS quality improvement and the law

Abrahamsen¹

2015

Emergency Medical Services

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Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach space Y is contained in a separable ideal in Y . We improve this result by replacing the term "ideal" with the term "almost isometric ideal". As a consequence of this we obtain, in terms of subspaces, characterizations of diameter 2 properties, the Daugavet property along with the properties of being an almost square space and an octahedral space.

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Strict u-ideals in Banach spaces

Cited by 7 publications

References 27 publications

Almost Isometric Ideals in Banach Spaces

Almost Isometric Ideals in Banach Spaces

Strict U-Ideals and U-Summands in Banach Spaces

EMS quality improvement and the law

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