Automatic continuity of biseparating maps

Araujo, Jesús; Jarosz, Krzysztof

doi:10.4064/sm155-3-3

Cited by 21 publications

(16 citation statements)

References 11 publications

(12 reference statements)

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“…As far as we know, even in this case our results are new, and the techniques in the proofs are nonstandard and nontrivial, compared to those in the literature [1,4,8,11] on separating or zero-product preservers (although some statements look similar). In a forthcoming paper, the authors will study the case where the underlying C * -algebra is not commutative.…”

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confidence: 93%

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Linear Orthogonality Preservers of Hilbert Bundles

Leung

Wong

2010

J. Aust. Math. Soc.

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A C-linear map θ (not necessarily bounded) between two Hilbert C * -modules is said to be 'orthogonality preserving' if θ(x), θ(y) = 0 whenever x, y = 0. We prove that if θ is an orthogonality preserving map from a full Hilbert C 0 ( )-module E into another Hilbert C 0 ( )-module F that satisfies a weaker notion of C 0 ( )-linearity (called 'localness'), then θ is bounded and there exists φ ∈ C b ( ) + such that θ (x), θ (y) = φ · x, y for all x, y ∈ E.2010 Mathematics subject classification: primary 46L08; secondary 46M20, 46H40, 46E40.

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confidence: 93%

“…We first recall two technical lemmas from [17, Lemmas 3.1 and 3.3, and Theorem 3.7] (see also [17,Remark 3.4]), which summarize, unify, and generalize techniques used sporadically in the literature [4,8,11]. …”

Section: Orthogonality Preserving Maps Between Hilbert C 0 ( )-Modulesmentioning

confidence: 99%

Linear Orthogonality Preservers of Hilbert Bundles

Leung

Wong

2010

J. Aust. Math. Soc.

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“…Their results apply to matrix algebras, standard operator algebras, C * -algebras and von Neumann algebras. J. Araujo and K. Jarosz established in [5] that every bijective linear map T between spaces of vector-valued continuous functions such that T and T −1 are multiplicative at zero is usually automatically continuous. The same authors prove in [4, Theorem 1] that every linear bijection T between standard operator algebras such that T and T −1 are multiplicative at zero is automatically continuous and a multiple of an algebra isomorphism.…”

Section: Introductionmentioning

confidence: 99%

Linear maps between C-algebras that are -homomorphisms at a fixed point

Burgos

Sánchez

Peralta

2018

Quaestiones Mathematicae

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Let A and B be C * -algebras. A linear map T : A → B is said to be a * -homomorphism at an elementAssuming that A is unital, we prove that every linear map T : A → B which is a * -homomorphism at the unit of A is a Jordan * -homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *homomorphism if and only if T is a * -homomorphism at the unit of A. For a general unital C * -algebra A and a linear map T : A → B, we prove that T is a * -homomorphism if, and only if, T is a * -homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a * -homomorphism at p and at 1 − p, then we prove that T is a Jordan * -homomorphism. We also study bounded linear maps that are * -homomorphisms at a unitary element in A.

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“…Hg(y) = 0 for all f, g ∈ C(X, E) and x ∈ X, y ∈ Y . The study of separating maps between different spaces of functions(as well as operator algebras) has attracted a considerable interest in resent years, see for example [4,6,8,17] and references therein. The well known results concerning separating maps from C(X) to C(Y ), for compact Hausdorff spaces X and Y , have been extended to not necessarily linear case in [5,16,17].…”

Section: Introductionmentioning

confidence: 99%

Fixed points of subadditive maps and some non-linear integral equations

Estaremi

Moeini

2017

J. Fixed Point Theory Appl.

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In this paper, first some results of [5] are extended for subadditive separating maps between C(X, E) and C(Y, E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed point. Finally as an application the existence and uniqueness of solution for a nonlinear integral equation is discussed.2010 Mathematics Subject Classification. 45G10, 37C25, 46J10. Key words and phrases. pointwise subadditive-strongly subadditive map-fixed point-integral equation.yousef estaremi

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Automatic continuity of biseparating maps

Abstract: Abstract. We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.

Cited by 21 publications

References 11 publications

Linear Orthogonality Preservers of Hilbert Bundles

Linear Orthogonality Preservers of Hilbert Bundles

Linear maps between C-algebras that are -homomorphisms at a fixed point

Fixed points of subadditive maps and some non-linear integral equations

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Automatic continuity of biseparating maps

Abstract: Abstract. We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.

Cited by 21 publications

References 11 publications

Linear Orthogonality Preservers of Hilbert Bundles

Linear Orthogonality Preservers of Hilbert Bundles

Linear maps between C*-algebras that are *-homomorphisms at a fixed point

Fixed points of subadditive maps and some non-linear integral equations

Contact Info

Product

Resources

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Linear maps between C-algebras that are -homomorphisms at a fixed point