Displaying similar documents to “Maps on idempotents”

Maps on idempotent operators

Peter Šemrl (2007)

Banach Center Publications

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The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver...

Turbulent maps and their ω-limit sets

F. Balibrea, C. La Paz (1997)

Annales Polonici Mathematici

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One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.

The set of automorphisms of B(H) is topologically reflexive in B(B(H))

Lajos Molnár (1997)

Studia Mathematica

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The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence ( Φ n ) of automorphisms of B(H) (depending on A) such that Φ ( A ) = l i m n Φ n ( A ) . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

Multi-invertible maps and their applications

Mirosław Ślosarski (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of r-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.

Spectra of the difference, sum and product of idempotents

Mohamed Barraa, Mohamed Boumazgour (2001)

Studia Mathematica

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We give a simple proof of the relation between the spectra of the difference and product of any two idempotents in a Banach algebra. We also give the relation between the spectra of their sum and product.

Automatic continuity of biseparating maps

Jesús Araujo, Krzysztof Jarosz (2003)

Studia Mathematica

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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.

On isomorphisms of standard operator algebras

Lajos Molnár (2000)

Studia Mathematica

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We show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.

On the structure of positive maps between matrix algebras

Władysław A. Majewski, Marcin Marciniak (2007)

Banach Center Publications

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The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.

Diameter-preserving maps on various classes of function spaces

Bruce A. Barnes, Ashoke K. Roy (2002)

Studia Mathematica

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Under some mild assumptions, non-linear diameter-preserving bijections between (vector-valued) function spaces are characterized with the help of a well-known theorem of Ulam and Mazur. A necessary and sufficient condition for the existence of a diameter-preserving bijection between function spaces in the complex scalar case is derived, and a complete description of such maps is given in several important cases.

Idempotent operators on a finite chain.

Margalida Mas Grimalt, Joan Torrens, Tomasa Calvo, Marc Carbonell (1999)

Mathware and Soft Computing

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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.