A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices

In this paper we consider the question when a triangularizable semigroup S of positive compact ideal-triangularizable operators on an order continuous Banach lattice X is ideal-triangularizable. We prove that triangularizability always implies ideal-triangularizability iff X contains at most one ato...

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Main Author:	Kandić M.
Format:	Article
Language:	English
Published:	De Gruyter 2018-09-01
Series:	Special Matrices
Subjects:	banach lattices positive operators triangularizability stable spectrum
Online Access:	https://doi.org/10.1515/spma-2018-0029

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spelling	doaj-78f59d68a64b4759ac30e7ffd0e701862021-10-02T18:54:20ZengDe GruyterSpecial Matrices2300-74512018-09-016136937510.1515/spma-2018-0029spma-2018-0029A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach LatticesKandić M.0Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19,Ljubljana, SlovenijaIn this paper we consider the question when a triangularizable semigroup S of positive compact ideal-triangularizable operators on an order continuous Banach lattice X is ideal-triangularizable. We prove that triangularizability always implies ideal-triangularizability iff X contains at most one atom. Under this condition we connect ideal-triangularizability of S with spectral properties of S. Surprisingly, S is idealtriangularizable iff the spectral radius is subadditive on S iff the spectral radius is submultiplicative on S. We also consider a pair of positive compact operators A and T with the property that A has a T-stable spectrum.https://doi.org/10.1515/spma-2018-0029banach latticespositive operatorstriangularizabilitystable spectrum
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Kandić M.
spellingShingle	Kandić M. A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices Special Matrices banach lattices positive operators triangularizability stable spectrum
author_facet	Kandić M.
author_sort	Kandić M.
title	A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices
title_short	A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices
title_full	A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices
title_fullStr	A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices
title_full_unstemmed	A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices
title_sort	note on spectral sublinearity for collections of positive compact operators on banach lattices
publisher	De Gruyter
series	Special Matrices
issn	2300-7451
publishDate	2018-09-01
description	In this paper we consider the question when a triangularizable semigroup S of positive compact ideal-triangularizable operators on an order continuous Banach lattice X is ideal-triangularizable. We prove that triangularizability always implies ideal-triangularizability iff X contains at most one atom. Under this condition we connect ideal-triangularizability of S with spectral properties of S. Surprisingly, S is idealtriangularizable iff the spectral radius is subadditive on S iff the spectral radius is submultiplicative on S. We also consider a pair of positive compact operators A and T with the property that A has a T-stable spectrum.
topic	banach lattices positive operators triangularizability stable spectrum
url	https://doi.org/10.1515/spma-2018-0029
work_keys_str_mv	AT kandicm anoteonspectralsublinearityforcollectionsofpositivecompactoperatorsonbanachlattices AT kandicm noteonspectralsublinearityforcollectionsofpositivecompactoperatorsonbanachlattices
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A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices

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