HOLOMORPHIC FAMILIES OF LINEAR OPERATORS IN BANACH SPACES

Victor Borisov; Noboru Okazawa

doi:10.55937/sut/1262184328

June 1997 HOLOMORPHIC FAMILIES OF LINEAR OPERATORS IN BANACH SPACES

Victor Borisov, Noboru Okazawa

Author Affiliations +

SUT J. Math. 33(2): 189-205 (June 1997). DOI: 10.55937/sut/1262184328

Abstract

Given two closed linear operators T and A in a Banach space, a sufficient condition is presented for the family $\{ T(\kappa );{\rm{Re}}\;\kappa \; > a\} = \{ T + \kappa A;{\rm{Re}}\;\kappa > a\} ,a \in {\rm{R}}$ , to be holomorphic of type (A). Detailed results are established when T and A are m-accretive in a reflexive Banach space. The results restricted to the Hilbert space case are almost identical with Kato’s. As an application a simple first-order singular differential operator in the ${L^p}$ -space $(1 < p < \infty )$ is discussed. This is a generalization of Kato’s result in the ${L^2}$ -case.

Acknowledgement

The authors would like to thank the referee for his careful reading of the manuscript.

Citation

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Victor Borisov. Noboru Okazawa. "HOLOMORPHIC FAMILIES OF LINEAR OPERATORS IN BANACH SPACES." SUT J. Math. 33 (2) 189 - 205, June 1997. https://doi.org/10.55937/sut/1262184328

Information

Received: 27 September 1997; Published: June 1997

First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1262184328

Subjects:

Primary: 47A56

Secondary: 47B44

Keywords: Closed linear operators , duality maps , holomorphic families of type (A) , m-accretive operators , singular differential operators of first-order

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