Microspectral analysis of quasinilpotent operators

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Microspectral analysis of quasinilpotent operators. / Malinen, Jarmo; Nevanlinna, Olavi; Zemánek, Jaroslav .

In: BANACH CENTER PUBLICATIONS, Vol. 112, 2017, p. 281-306.

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@article{becae95034e047c7b7db7a3359c09821,
title = "Microspectral analysis of quasinilpotent operators",
abstract = "We develop a microspectral theory for quasinilpotent linear operators Q (i.e., those with σ(Q)={0}) in a Banach space. For such operators, the classical spectral theory gives little information. Deeper structure can be obtained from microspectral sets in C as defined below. Such sets describe, e.g., semigroup generation, various resolvent properties, power boundedness as well as Tauberian properties associated to zQ for z∈C.",
author = "Jarmo Malinen and Olavi Nevanlinna and Jaroslav Zem{\'a}nek",
year = "2017",
doi = "10.4064/bc112-0-15",
language = "English",
volume = "112",
pages = "281--306",
journal = "BANACH CENTER PUBLICATIONS",
issn = "0137-6934",

}

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TY - JOUR

T1 - Microspectral analysis of quasinilpotent operators

AU - Malinen, Jarmo

AU - Nevanlinna, Olavi

AU - Zemánek, Jaroslav

PY - 2017

Y1 - 2017

N2 - We develop a microspectral theory for quasinilpotent linear operators Q (i.e., those with σ(Q)={0}) in a Banach space. For such operators, the classical spectral theory gives little information. Deeper structure can be obtained from microspectral sets in C as defined below. Such sets describe, e.g., semigroup generation, various resolvent properties, power boundedness as well as Tauberian properties associated to zQ for z∈C.

AB - We develop a microspectral theory for quasinilpotent linear operators Q (i.e., those with σ(Q)={0}) in a Banach space. For such operators, the classical spectral theory gives little information. Deeper structure can be obtained from microspectral sets in C as defined below. Such sets describe, e.g., semigroup generation, various resolvent properties, power boundedness as well as Tauberian properties associated to zQ for z∈C.

U2 - 10.4064/bc112-0-15

DO - 10.4064/bc112-0-15

M3 - Article

VL - 112

SP - 281

EP - 306

JO - BANACH CENTER PUBLICATIONS

JF - BANACH CENTER PUBLICATIONS

SN - 0137-6934

ER -

ID: 16528289