Characterization of unbounded spectral operators with spectrum in a half-line

Shmuel Kantorovitz

doi:10.1007/bf02566207

Characterization of unbounded spectral operators with spectrum in a half-line

Shmuel Kantorovitz

Department of Mathematics

Temple University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let T be a possibly unbounded linear operator in the Banach space X such that R(t)=(t+T)^-1 is defined on R⁺. Let S=TR(I-TR) and let B(.,.) denote the Beta function. Theorem 1.1. T is a scalar-type spectral operator with spectrum in [0, ∞) if and only if {Mathematical expression} A "local" version of this result is formulated in Theorem 2.2.

Original language	English
Pages (from-to)	163-178
Number of pages	16
Journal	Commentarii Mathematici Helvetici
Volume	56
Issue number	1
DOIs	https://doi.org/10.1007/bf02566207
State	Published - Dec 1981

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AB - Let T be a possibly unbounded linear operator in the Banach space X such that R(t)=(t+T)-1 is defined on R +. Let S=TR(I-TR) and let B(.,.) denote the Beta function. Theorem 1.1. T is a scalar-type spectral operator with spectrum in [0, ∞) if and only if {Mathematical expression} A "local" version of this result is formulated in Theorem 2.2.

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Characterization of unbounded spectral operators with spectrum in a half-line

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