(S+N)‐triangular operators: spectral properties and important examples. Issue 13 (18th January 2016)

• Record Type: Journal Article
• Authors: Sakhnovich, Lev
• Is Part Of: Mathematische Nachrichten. Volume 289:Issue 13(2016)
• Page Start: 1680
• Page End: 1691
• Publication Date: 2016-01-18
• Subjects: Maximal chain of orthogonal projections -- invariant subspace -- triangular representation -- spectral operator -- 47A15 -- 47A45 -- 47A46; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500064
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : We introduce a notion of ( S + N ) ‐triangular operators in the Hilbert space using some basic ideas from triangular representation theory. Our notion generalizes the well‐known notion of the spectral operators so that many properties of the ( S + N ) ‐triangular operators coincide with those of spectral operators. At the same time we show that wide classes of operators are ( S + N ) ‐triangular.