Spaceability of the sets of surjective and injective operators between sequence spaces

Diniz, Diogo; Fávaro, Vinícius V.; Pellegrino, Daniel; Raposo, Anselmo

doi:10.1007/s13398-020-00922-3

Cited by 10 publications

(6 citation statements)

References 12 publications

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“…So, equality (11) collapses to ∞ j=2 a j f j−1 = 0. The same reasoning we made in (8) allows us to conclude that a j = 0 for every j.…”

Section: Resultsmentioning

confidence: 60%

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Spaceability of sets of p-compact maps

Alves

Turco

2022

Journal of Mathematical Analysis and Applications

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“…So, equality (11) collapses to ∞ j=2 a j f j−1 = 0. The same reasoning we made in (8) allows us to conclude that a j = 0 for every j.…”

Section: Resultsmentioning

confidence: 60%

“…Pointwise lineability and (1, c)-lineability of sets of injective/non-injective bounded linear operators between classical spaces were studied in [7,8,10]. The purpose of this paper is to generalize, in several directions, the result we state next.…”

Section: Introductionmentioning

confidence: 92%

Spaceability of sets of p-compact maps

Alves

Turco

2022

Journal of Mathematical Analysis and Applications

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“…Recently, some results in this direction have been obtained covered under the veil of (1, β)-lineability/spaceability. Analyzing the proof of [12,Theorem 1.3] we conclude that, in fact, we have pointwise lineability/spaceability result.…”

Section: Pointwise Spaceability In Sequence Spacesmentioning

confidence: 69%

Pointwise Lineability in Sequence Spaces

Pellegrino¹,

Raposo²

2020

Preprint

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“…For instance, the interested reader may consult [2,5,9,27,33,34,47]. For more on the property of (α, β)-spacebility applied to families of operators, see [22,23].…”

Section: Lineability and Spaceabilitymentioning

confidence: 99%

On the Existence of Non-Norm-Attaining Operators

Dantas¹,

Jung

Martínez-Cervantes³

2021

J. Inst. Math. Jussieu

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In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in $\mathcal {L}(E, F)$ . By using a theorem due to Pfitzner on James boundaries, we show that if there exists a relatively compact set K of $\mathcal {L}(E, F)$ (in the weak operator topology) such that $0$ is an element of its closure (in the weak operator topology) but it is not in its norm-closed convex hull, then we can guarantee the existence of an operator that does not attain its norm. This allows us to provide the following generalisation of results due to Holub and Mujica. If E is a reflexive space, F is an arbitrary Banach space and the pair $(E, F)$ has the (pointwise-)bounded compact approximation property, then the following are equivalent: (i) $\mathcal {K}(E, F) = \mathcal {L}(E, F)$ ; (ii) Every operator from E into F attains its norm; (iii) $(\mathcal {L}(E,F), \tau _c)^* = (\mathcal {L}(E, F), \left \Vert \cdot \right \Vert )^*$ , where $\tau _c$ denotes the topology of compact convergence. We conclude the article by presenting a characterisation of the Schur property in terms of norm-attaining operators.

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Spaceability of the sets of surjective and injective operators between sequence spaces

Cited by 10 publications

References 12 publications

Spaceability of sets of p-compact maps

Spaceability of sets of p-compact maps

Pointwise Lineability in Sequence Spaces

On the Existence of Non-Norm-Attaining Operators

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