2-Local derivations and automorphisms on $B(H)$
Sh. A. AyupovInstitute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Dormon yoli 29, 100125 Tashkent, UzbekistanKarimbergen KudaybergenovDepartment of Mathematics, Karakalpak State University, Ch. Abdirov 1, 230113, Nukus, Uzbekistan
ABI
Abstract
The paper is devoted to 2-local derivations and 2-local automorphisms on the algebra $B(H)$ of all bounded linear operators on a Hilbert space $H.$ We prove that every 2-local derivation on $B(H)$ is a derivation. A similar result is obtained for automorphisms.