Erratum to “Can ever be amenable?” (Studia Math. 188 (2008), 151-174)
In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since our structural...
It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form . The proof appeals to the monogenic functional calculus.
We review several results on interpolation of Banach algebras and factorization of weakly compact homomorphisms. We also establish a new result on interpolation of multilinear operators.