Bounds for Uniform Resolvent Conditions
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Abstract
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.
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References
Y. CHEN, Sur les multifonctions analytiques et la théorie spectrale, doctoral dissertation (2000), Laval University.
C. Lubich and O. Nevanlinna, On resolvent conditions and stability estimates, BIT 31 (1991), 293–313.
O. Nevanlinna, On the growth of the resolvent operators for power bounded operators, Banach Center Publications, 38 (1997), 247–264.
O. Nevanlinna, Resolvent conditions and powers of operators, Studia Mathematica, 145 (2001), 113-134.
E. Wegert and L. N. Trefethen, From the Buffon Needle Problem to the Kreiss Matrix Theorem, The American Mathematical Monthly, 101 (1994), 132–139