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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F03%3A00106806%21RIV%2F2005%2FGA0%2FA05005%2FN
rdf:type
n3:Vysledek skos:Concept
dcterms:description
Podle známé věty ( Brown-Chevreau-Pearcy ) každá kontrakce na Hilbertově prostoru, jejíž spektrum obsahuje jednotkovou kružnici, má netriviální invariantní podprostor. Tj. existuje nenulový necyklický vektor. Zde je ukázáno, že každý operátor s ohraničenými mocninami, jehož spektrální poloměr je roven 1, má nenulový vektor, který není supercyklický. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset.
dcterms:title
Operátory s ohraničenými mocninami a supercyklické vektory Power bounded operators and supercyclic vectors Power bounded operators and supercyclic vectors
skos:prefLabel
Power bounded operators and supercyclic vectors Power bounded operators and supercyclic vectors Operátory s ohraničenými mocninami a supercyklické vektory
skos:notation
RIV/67985840:_____/03:00106806!RIV/2005/GA0/A05005/N
n4:strany
3807;3812
n4:aktivita
n11:Z n11:P
n4:aktivity
P(GA201/03/0041), Z(AV0Z1019905)
n4:cisloPeriodika
12
n4:dodaniDat
n16:2005
n4:domaciTvurceVysledku
n8:8840199
n4:druhVysledku
n14:J
n4:duvernostUdaju
n9:S
n4:entitaPredkladatele
n17:predkladatel
n4:idSjednocenehoVysledku
622169
n4:idVysledku
RIV/67985840:_____/03:00106806
n4:jazykVysledku
n18:eng
n4:klicovaSlova
supercyclic vector;invariant subspace problem;power bounded operator
n4:klicoveSlovo
n15:power%20bounded%20operator n15:supercyclic%20vector n15:invariant%20subspace%20problem
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[F5716B5E43A6]
n4:nazevZdroje
Proceedings of the American Mathematical Society
n4:obor
n5:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:projekt
n10:GA201%2F03%2F0041
n4:rokUplatneniVysledku
n16:2003
n4:svazekPeriodika
131
n4:tvurceVysledku
Müller, Vladimír
n4:zamer
n13:AV0Z1019905
s:issn
0002-9939
s:numberOfPages
6