Back to Search
Start Over
On higher order selfadjoint operators.
- Source :
-
Linear Algebra & its Applications . Feb2020, Vol. 587, p358-386. 29p. - Publication Year :
- 2020
-
Abstract
- For a positive integer m and a Hilbert space H an operator T in B (H) , the space of all bounded linear operators on H , is called m -selfadjoint if ∑ k = 0 m (− 1) k ( m k ) T ⁎ k T m − k = 0. In this paper, we show that if T ∈ B (H) and the spectrum of T consists of a finite number of points then it is m -selfadjoint if and only if it is an n -Jordan operator for some integer n. Moreover, we prove that if T is m -selfadjoint then T is nilpotent when it is quasinilpotent. Then we characterize m -selfadjoint weighted shift operators. Also, we show that if T is m -selfadjoint then so is p (T) when p (z) is a polynomial with real coefficients. After that, we investigate an elementary operator τ and a generalized derivation operator δ on the Hilbert-Schmidt class C 2 (H) which are m -selfadjoint. Finally, we prove that no m -selfadjoint operator on an infinite-dimensional Hilbert space, can be N -supercyclic, for any N ≥ 1. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SELFADJOINT operators
*HILBERT space
*LINEAR operators
*INTEGERS
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 587
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 140334331
- Full Text :
- https://doi.org/10.1016/j.laa.2019.11.009