AMENABLE BANACH ALGEBRA AND SCALAR-TYPE SPECTRAL OPERATORS

Abstract. Willis showed that, if T is a compact operator on Hilbert space and AT is amenable, then T is scalar-type spectral operator. The properties of Hilbert spaces are used in essential way at several points in the Willis proof and it does not work for Banach spaces. By an Example we will show that there is a compact operator T on a Banach Space X such that AT is amenable, and T is not scalar type Spectral. This answers a question raised by wellis.

کلیدواژه ها:

Amenable Banach algebra ، compact operators ، scalar type spectral operators