Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions

Dubarbie, Luis

doi:10.4153/cmb-2010-035-7

Cited by 13 publications

(10 citation statements)

References 15 publications

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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: 57%

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

confidence: 57%

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

Dubarbie

2010

Positivity

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“…Following a very usual technique (see, for example, [9,11,12,44,45]), we can define a continuous support map ϕ : Z 1 ∪ Z 2 → L 1 . More concretely, for each s ∈ Z 1 ∪ Z 2 , we write supp(δ s T ) for the set of all t ∈ L 1 such that for each open set U ⊆ L 1 with t ∈ U there exists f ∈ C r (L 1 ) with coz( f ) ⊆ U and δ s (T ( f )) = 0.…”

Section: Orthogonality Preservers Between Commutative Real C * -Algebrasmentioning

confidence: 99%

“…It is easy to see that Z 3 is closed. Following a very usual technique (see, for example, [8,9,30,16] and [17]), we can define a continuous support map ϕ :…”

Section: Orthogonality Preservers Between Commutative Real C * -Algebrasmentioning

confidence: 99%

Orthogonal forms and orthogonality preservers on real function algebras

Garcés

Peralta

2013

Linear and Multilinear Algebra

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We initiate the study of orthogonal forms on a real C * -algebra. Motivated by previous contributions, due to Ylinen, Jajte, Paszkiewicz and Goldstein, we prove that for every continuous orthogonal form V on a commutative real C * -algebra, A, there exist functionals ϕ 1 and ϕ 2 in A * satisfyingfor every x, y in A. We describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between unital commutative real C * -algebras. As a consequence, we show that every orthogonality preserving linear bijection between unital commutative real C * -algebras is continuous.

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“…Similar results were given in [16] for such maps between vector-valued little Lipschitz function spaces. In [6], Dubarbie studied separating linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line.…”

Section: Introductionmentioning

confidence: 99%

Additive jointly separating maps and ring homomorphisms

Sady¹,

Tavani²

2019

Preprint

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A(X, E)−→C(Y, F ) is said to be jointly separating if coz(T f ) ∩ coz(Sg) = ∅ whenever coz(f )∩coz(g) = ∅. In this paper, first we give a partial description of additive jointly separating maps between certain spaces of vector-valued continuous functions (including spaces of vector-valued Lipschitz functions, absolutely continuous functions and continuously differentiable functions). Then we apply the results to characterize continuous ring homomorphisms between certain Banach algebras of vector-valued continuous functions. In particular, the results provide some generalizations of the recent results on unital homomorphisms between vector-valued Lipschitz algebras, with a different approach.

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Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions

Cited by 13 publications

References 15 publications

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

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

Orthogonal forms and orthogonality preservers on real function algebras

Additive jointly separating maps and ring homomorphisms

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