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Rank-permutable additive mappings

✍ Scribed by A.A. Alieva; A.E. Guterman; B. Kuzma

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
151 KB
Volume
414
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let Οƒ be a fixed non-identical permutation on k elements. Additive bijections T on the matrix algebra M n (F) over a field F of characteristic zero, with the property that rk

implies the same condition on the T images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.

πŸ“œ SIMILAR VOLUMES

Additive mappings that preserve rank one
Additive mappings that preserve rank one nilpotent operators
✍ Wu Jing; Pengtong Li; Shijie Lu πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 113 KB

Let B(X) be the algebra of bounded operators on a complex infinite dimensional Banach space X, and F (X) be the subalgebra of all finite rank operators in B(X). A characterization of additive mappings on F (X) which preserve rank one nilpotent operators in both directions is given. As applications o