No abstract

It is shown that the joint spectral radius ρ(M ) of a precompact set M of operators on a Banach space equals the maximum of two numbers, the joint spectral radius ρ e (M ) of the image of M in the Calkin algebra and the BW-radius r(M ). Similar results related to general normed algebras are also obtained. The proofs are based on the theory of topological radicals of normed algebras.

We develop the tensor spectral radius technique and the theory of the tensor radical. Basing on them we obtain several results on spectra of multiplication operators on Banach bimodules and indicate some applications to the spectral theory of elementary and multiplication operators on Banach algebras and modules with various compactness properties. ContentsVICTOR S. SHULMAN AND YURII V. TUROVSKII 6.2. Invariant subspaces for operators on an ordered pair of Banach spaces 51 6.3. Semicompact multiplication operators 52 6.4. Semicompact elementary operators 55 References 61