Spectra, tensor products, and linear operator equations

Mary Rodriguez Embry and Marvin Rosenblum

Vol. 53 (1974), No. 1, 95–107

DOI: 10.2140/pjm.1974.53.95

Abstract

Suppose X₁ and X₂ are complex Banach spaces with u₀,⋯ , u_n in ℒ(X₁),v ∈ℒ(X₂), and suppose ⊗ is a uniform crossnorm. The spectra of the operators ∑ _j=0ⁿu_f ⊗ v^j on X₁ ⊗ X₂ and R : x →∑ _j=0ⁿu_jxv^f,x ∈ℒ(X₂,X₁), are studied in the context of a general theory. Explicit representations are set down for the resolvents of these and more general operators.

Mathematical Subject Classification 2000

Primary: 47A60

Secondary: 46H05

Milestones

Received: 24 July 1973

Published: 1 July 1974