Some characterizations of the automorphisms of B(H) and C(X)

By Lajos Molnár. 2000

157 citations recorded by the source corpus.

We present some nonlinear characterizations of the automorphisms of the operator algebra B(H) and the function algebra C(X) by means of their spectrum preserving properties.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d998f61cecffb8738d267f285cd6283d60ff6bbd

How researchers see this paper

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In Algebra and Number Theory

1. Hiroyuki Takagi
2. Osamu Hatori
3. Takeshi Miura
4. N. V. Rao
5. A. Roy
6. Chi-Kwong Li
7. J. Chan
8. Nung-Sing Sze

In Computational Theory and Mathematics

1. N. V. Rao
2. A. Roy
3. Osamu Hatori
4. Takeshi Miura
5. Hiroyuki Takagi
6. Chi-Kwong Li
7. J. Chan
8. Nung-Sing Sze

In Geometry and Topology

1. Hiroyuki Takagi
2. Osamu Hatori
3. Takeshi Miura
4. N. V. Rao
5. A. Roy
6. J. Chan
7. Nung-Sing Sze
8. Chi-Kwong Li

Citations in the corpus

• Local automorphisms of operator algebras on Banach spaces (2002, background): “We mention that similar characterizations of the automorphisms of operator algebras and of function algebras can be found in [4] but there we had to assume that the transformations in question are all surjective.”
• Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties (2006, background): “is assumed in Theorem 6 of [3], can be removed.”
• MULTIPLICATIVELY SPECTRUM-PRESERVING MAPS OF FUNCTION ALGEBRAS. II (2005, methodology): “After characterizing the points of the Choquet boundary as strong boundary points, we use this equivalence to provide a natural extension of the theorem in [10], which, in turn, was inspired by the main result in [6], by proving the ‘Main Theorem’: if Φ : A → A is a surjective map with the property ”
• Maps preserving numerical ranges of operator products (2005, unknown): “Molnár [10], who characterized surjective maps φ on B(H) such that σ(φ(A)φ(B)) = σ(AB) for all A, B ∈ B(H).”
• Maps preserving the idempotency of products of operators (2007, background): “Motivated by problems concerning local automorphisms Molnár [11, 12] studied maps preserving the spectrum of operator or matrix products (for related results see [5, 6]).”
• Mappings preserving spectra of products of matrices (2007, background): “In [6] Molnár studied surjective maps φ on bounded linear operators such that”
• Mappings on matrices: invariance of functional values of matrix products (2006, unknown): “see [6, 13, 14, 19].”
• Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative (2007, methodology): “Then theorems of Molnár and their generalizations were proved in a way similar to the proof of Theorem 3.1.”