Bounds for uniform resolvent conditions

  • Yin Chen Lakehead University
Keywords: resolvent condition, absolute summability of powers of operator, spectrum of operator


For a bounded linear operator on a Banach space, the uniform resolvent condition implies the absolute summability of the powers of the operator. In this paper, we study the bounds for the absolute sum of the powers of an operator that satisfies the uniform resolvent condition. Some known bounds on general Banach spaces as well as on finite-dimensional Banach spaces are improved.
How to Cite
Chen, Y. (2020). Bounds for uniform resolvent conditions. Tamkang Journal of Mathematics, 51(1).