Geodesic
Classes of operators related to 2-isometric operators
Filomat, Tome 36 (2022) no. 11, p. 3809

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DOI

We introduce the class of quasi-square-2-isometric operators on a complex separable Hilbert space. This class extends the class of 2-isometric operators due to Agler and Stankus. An operator T is said to be quasi-square-2-isometric if T * 5 T 5 − 2T * 3 T 3 + T * T = 0. In this paper, we give operator matrix representation of quasi-square-2-isometric operator in order to obtain spectral properties of this operator. In particular, we show that the function σ is continuous on the class of all quasi-square-2-isometric operators. Under the hypothesis σ(T) ∩ (−σ(T)) = ∅, we also prove that if E T ({λ}) is the Riesz idempotent for an isolated point of the spectrum of quasi-square-2-isometric operator, then E T ({λ}) is self-adjoint.
DOI : 10.2298/FIL2211809Z
Classification : 47B20, 47A10
Keywords: Square-2-isometric operator, Quasi-square-2-isometric operator, Spectral continuity, Invariant subspace, Riesz idempotent 
Fei Zuo; Junli Shen; Alatancang Chen. Classes of operators related to 2-isometric operators. Filomat, Tome 36 (2022) no. 11, p. 3809 . doi: 10.2298/FIL2211809Z
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     title = {Classes of operators related to 2-isometric operators},
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     doi = {10.2298/FIL2211809Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2211809Z/}
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