On quasi-similarity and putnam-fuglede property of operators in Hilbert spaces

Abstract

The problem of finding conditions under which two given operators say A and B have equal spectra has been considered by several authors. In this paper we show that quasi-similar operators 𝐴 and 𝐵 which satisfy the Putnam- Fuglede property have equal spactra and also equal essential spectra. AMS subject classification: 47B47, 47A30, 47B20.