Abstract. An operator T on a complex Hilbert space is called a 2-isometry if
T*2 T2 - 2T* T + I = 0.Our underlying purpose in this article is to investigate some algebraic and spectral properties of 2-isometries.
2000 Mathematics Subject Classification. 47A62, 47A63.
Key words and phrases. Hilbert space, 2-isometry, spectrum.