Weobtaintheadmissiblesetsontheunitcircletobethespectrumofastrict m-isometryonann-finitedimensionalHilbertspace.Thispropertygivesabetterpictureof thecorrectspectrumofanm-isometry.Wedeterminethattheonlym-isometriesonR2are 3-isometriesandisometriesgivingby±I+Q,whereQisanilpotentoperator.Moreover, onrealHilbertspace,weobtainthatm-isometriespreservevolumes.Alsowepresentaway toconstructastrict(m+1)-isometrywithanm-isometrygiven,usingideasofAlemanand Suciu[7,Proposition5.2]oninfinitedimensionalHilbertspace.
