Biseparating maps between Lipschitz function spaces

Araujo, Jesús; Dubarbie, Luis

doi:10.1016/j.jmaa.2009.03.065

Cited by 25 publications

(23 citation statements)

References 24 publications

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“…[14], [3], [7], [15] or [12]), on group algebras of locally compact Abelian groups ( [8]), on Fourier algebras ( [10] and [20]) and on some others (see e.g. [16], [17] or [5]). …”

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confidence: 99%

Disjointness preserving mappings on BSE Ditkin algebras

Font¹

2011

Publ. Math. Debrecen

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Let A and B be regular Banach function algebras. A linear map T defined from A into B is said to be disjointness preserving or sepa-We prove that if there exists a disjointness preserving bijection between two BSE Ditkin algebras with a BAI, then they are isomorphic as algebras. As a corollary we can deduce that two of these algebras are algebraically isomorphic if there exists a surjective isometry between them for the supremum norm.

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“…[14], [3], [7], [15] or [12]), on group algebras of locally compact Abelian groups ( [8]), on Fourier algebras ( [10] and [20]) and on some others (see e.g. [16], [17] or [5]). …”

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confidence: 99%

Disjointness preserving mappings on BSE Ditkin algebras

Font¹

2011

Publ. Math. Debrecen

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“…Therefore, if we consider Context 1, the result is obtained applying [2,Corollaries 5.11 and 5.12]. For the second context, by Theorems 3.6 and 4.8 in [5], we conclude that T is continuous.…”

Section: Theorem 51 Let T :A(x E) → A(y F) Be a Bijective Linear Mmentioning

confidence: 78%

Maps preserving common zeros between subspaces of vector-valued continuous functions

Dubarbie

2010

Positivity

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For metric spaces X and Y , normed spaces E and F, and certain subspaces A(X, E) and A(Y, F) of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps T : A(X, E) → A(Y, F) preserving common zeros, that is, maps satisfying the property. Moreover, we provide some examples of subspaces for which the automatic continuity of linear bijections having the property (P) is derived.

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“…An argument similar to [2,Corollaries 5.11 and 5.12] shows that S has a closed graph. Now since S is additive and Q-homogeneous one can check easily that (as in the Closed Graph theorem, see, e.g., [10]) S is continuous.…”

Section: Jointly Common Zeros Preserving Maps Between Certain Subspacmentioning

confidence: 88%