A note on strong (skew) η-Lie products preserving maps on some algebras. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Taghavi, Ali; Kolivand, Farzaneh; Tavakoli, Ensiyeh
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 5(2019)
• Page Start: 886
• Page End: 895
• Publication Date: 2019-05-04
• Subjects: Preserving problems -- skew product maps -- C∗-algebras -- nest algebra; 46J10 -- 47B48 -- 47L35; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1435624
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: LetA be an arbitrary unital *-algebra over the real or complex fieldF, and letη ∈ F withη ≠ 1 . Assume thatΦ : A ⟶ A is a map. It is shown that, ifΦ satisfiesΦ ( A ) Φ ( P ) - η Φ ( P ) Φ ( A ) ∗ = A P - η P A ∗, for eachA ∈ A and projectionP ∈ } P 1, I - P 1 {, thenΦ ( I ) 2 = I andΦ ( A ) = A Φ ( I ) for allA ∈ A . Also, ifA is a nest algebra on Hilbert spaceH andΦ is a surjective map that satisfiesΦ ( A ) Φ ( P ) - Φ ( P ) Φ ( A ) = A P - P A, for eachA ∈ A and all idempotents P inA, then we characterize the concrete form ofΦ onA .