Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces
This Licentiate thesis consists of an introduction and three papers, which deal with some spaces of infinite matrices. In the introduction we give an overview of the area that serves as a frame for the rest of the thesis.In Paper 1 we introduce the space $B_w(\ell^2)$ of linear (unbounded) operators...
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Luleå tekniska universitet, Matematiska vetenskaper
2009
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ftluleatu:oai:DiVA.org:ltu-17166 2023-05-15T17:09:07+02:00 Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces Marcoci, Liviu-Gabriel 2009 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-17166 eng eng Luleå tekniska universitet, Matematiska vetenskaper Luleå Licentiate thesis / Luleå University of Technology, 1402-1757 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-17166 urn:isbn:978-91-86233-38-9 Local 1fe59bb0-3003-11de-bd0f-000ea68e967b info:eu-repo/semantics/openAccess Mathematical Analysis Matematisk analys Licentiate thesis, comprehensive summary info:eu-repo/semantics/masterThesis text 2009 ftluleatu 2022-10-25T20:50:58Z This Licentiate thesis consists of an introduction and three papers, which deal with some spaces of infinite matrices. In the introduction we give an overview of the area that serves as a frame for the rest of the thesis.In Paper 1 we introduce the space $B_w(\ell^2)$ of linear (unbounded) operators on $\ell^2$ which map decreasing sequences from $\ell^2$ into sequences from $\ell^2$ and we find some classes of operators belonging either to $B_w(\ell^2)$ or to the space of all Schur multipliers on $B_w(\ell^2)$.In Paper 2 we further continue the study of the space $B_w(\ell^p)$ in the range $1 <\infty$. In particular, we characterize the upper triangular positive matrices from $B_w(\ell^p)$.In Paper 3 we prove a new characterization of the Bergman-Schatten spaces $L_a^p(D,\ell^2)$, the space of all upper triangular matrices such that $\|A(\cdot)\|_{L^p(D,\ell^2)}<\infty$, where \[\|A(r)\|_{L^p(D,\ell^2)}=\left(2\int_0^1\|A(r)\|^p_{C_p}rdr\right)^\frac{1}{p}. \]This characterization is similar to that for the classical Bergman spaces. We also prove a duality between the little Bloch space and the Bergman-Schatten classes in the case of infinite matrices. Godkänd; 2009; 20090423 (livmar); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Tisdag den 2 juni 2009 kl 10.15 Plats: D 2214, Luleå tekniska universitet Master Thesis Luleå Luleå Luleå University of Technology Publications (DiVA) Persson ENVELOPE(-58.400,-58.400,-64.200,-64.200) |
institution |
Open Polar |
collection |
Luleå University of Technology Publications (DiVA) |
op_collection_id |
ftluleatu |
language |
English |
topic |
Mathematical Analysis Matematisk analys |
spellingShingle |
Mathematical Analysis Matematisk analys Marcoci, Liviu-Gabriel Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces |
topic_facet |
Mathematical Analysis Matematisk analys |
description |
This Licentiate thesis consists of an introduction and three papers, which deal with some spaces of infinite matrices. In the introduction we give an overview of the area that serves as a frame for the rest of the thesis.In Paper 1 we introduce the space $B_w(\ell^2)$ of linear (unbounded) operators on $\ell^2$ which map decreasing sequences from $\ell^2$ into sequences from $\ell^2$ and we find some classes of operators belonging either to $B_w(\ell^2)$ or to the space of all Schur multipliers on $B_w(\ell^2)$.In Paper 2 we further continue the study of the space $B_w(\ell^p)$ in the range $1 <\infty$. In particular, we characterize the upper triangular positive matrices from $B_w(\ell^p)$.In Paper 3 we prove a new characterization of the Bergman-Schatten spaces $L_a^p(D,\ell^2)$, the space of all upper triangular matrices such that $\|A(\cdot)\|_{L^p(D,\ell^2)}<\infty$, where \[\|A(r)\|_{L^p(D,\ell^2)}=\left(2\int_0^1\|A(r)\|^p_{C_p}rdr\right)^\frac{1}{p}. \]This characterization is similar to that for the classical Bergman spaces. We also prove a duality between the little Bloch space and the Bergman-Schatten classes in the case of infinite matrices. Godkänd; 2009; 20090423 (livmar); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Tisdag den 2 juni 2009 kl 10.15 Plats: D 2214, Luleå tekniska universitet |
format |
Master Thesis |
author |
Marcoci, Liviu-Gabriel |
author_facet |
Marcoci, Liviu-Gabriel |
author_sort |
Marcoci, Liviu-Gabriel |
title |
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces |
title_short |
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces |
title_full |
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces |
title_fullStr |
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces |
title_full_unstemmed |
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces |
title_sort |
some new results concerning schur multipliers and duality results between bergman-schatten and little bloch spaces |
publisher |
Luleå tekniska universitet, Matematiska vetenskaper |
publishDate |
2009 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-17166 |
long_lat |
ENVELOPE(-58.400,-58.400,-64.200,-64.200) |
geographic |
Persson |
geographic_facet |
Persson |
genre |
Luleå Luleå |
genre_facet |
Luleå Luleå |
op_relation |
Licentiate thesis / Luleå University of Technology, 1402-1757 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-17166 urn:isbn:978-91-86233-38-9 Local 1fe59bb0-3003-11de-bd0f-000ea68e967b |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1766065039115026432 |