Translator Disclaimer
Winter 2019 Norm estimates for resolvents of linear operators in a Banach space and spectral variations
Michael Gil'
Adv. Oper. Theory 4(1): 113-139 (Winter 2019). DOI: 10.15352/aot.1801-1293

Abstract

Let $P_t$ $(a\le t\le b)$ be a function whose values are projections in a Banach space. The paper is devoted to bounded linear operators $A$ admitting the representation $$A=\int_a^b \phi(t)dP_{t}+V,$$ where $\phi(t)$ is a scalar function and $V$ is a compact quasi-nilpotent operator such that $P_tVP_t=VP_t$ $(a\le t\le b)$. We obtain norm estimates for the resolvent of $A$ and a bound for the spectral variation of $A$. In addition, the representation for the resolvents of the considered operators is established via multiplicative operator integrals. That representation can be considered as a generalization of the representation for the resolvent of a normal operator in a Hilbert space. It is also shown that the considered operators are Kreiss-bounded. Applications to integral operators in $L^p$ are also discussed. In particular, bounds for the upper and lower spectral radius of integral operators are derived.

Citation

Download Citation

Michael Gil'. "Norm estimates for resolvents of linear operators in a Banach space and spectral variations." Adv. Oper. Theory 4 (1) 113 - 139, Winter 2019. https://doi.org/10.15352/aot.1801-1293

Information

Received: 11 January 2018; Accepted: 13 April 2018; Published: Winter 2019
First available in Project Euclid: 27 April 2018

zbMATH: 06946446
MathSciNet: MR3867337
Digital Object Identifier: 10.15352/aot.1801-1293

Subjects:
Primary: 47A10
Secondary: 47A11, 47A30, 47A55, 47G10

Rights: Copyright © 2019 Tusi Mathematical Research Group

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.4 • No. 1 • Winter 2019
Back to Top