Local automorphisms of operator algebras on Banach spaces

By Lajos Molnár. 2002

56 citations recorded by the source corpus.

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d9b6ed96700542f5b8dbeaa31a0be9f64b7d6b63

How researchers see this paper

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In Algebra and Number Theory

1. Sh. A. Ayupov
2. K. Kudaybergenov
3. Guoxing Ji
4. Gorazd Lešnjak
5. M. Dobovišek
6. J. Chan
7. Nung-Sing Sze
8. Li Fang

In Applied Mathematics

1. Sh. A. Ayupov
2. J. Chan
3. Nung-Sing Sze
4. Chi-Kwong Li
5. K. Kudaybergenov

In Mathematical Physics

1. Sh. A. Ayupov
2. K. Kudaybergenov
3. Gorazd Lešnjak
4. M. Dobovišek
5. J. Chan
6. Nung-Sing Sze
7. Chi-Kwong Li
8. Bojan Kuzma

Citations in the corpus

• 2-Local derivations and automorphisms on B(H) (2011, background): “A similar description for the finite-dimensional case appeared later in [7], [11].”
• 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 that preserve pairs of operators with zero triple Jordan product (2007, background): “Motivated by theory and applications, many authors have studied mappings on matrices or operators leaving invariant certain subsets, functions, and relations; for example, see [4, 10, 12, 14] and their references.”
• Mappings on matrices: invariance of functional values of matrix products (2006, unknown): “see [6, 13, 14, 19].”
• Mappings preserving spectra of products of matrices (2007, background): “Note that a characterization of those φ : Mn → Mn such that AB and φ(A)φ(B) have the same eigenvalues counting multiplicities is given in [7].”