Reflexivity defect of spaces of linear operators

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Title:	Reflexivity defect of spaces of linear operators
Authors:	ID Bračič, Janko (Author) ID Kuzma, Bojan (Author)
Files:	http://dx.doi.org/10.1016/j.laa.2008.07.024
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	For a finite-dimensional linear subspace ▫{ $\mathscr{S}} \subseteq {\mathscr{L}} (V,W)$ ▫ and a positive integer $k$ , the $k$ -reflexivity defect of $\mathscr{S}$ is defined by ${\mathrm{rd}}_k ({\mathscr{S}}) = \dim({\mathrm{Ref}}_k (\mathscr{S})/\mathscr{S})$ where ${\mathrm{Ref}}_k$ is the $k$ -reflexive closure of $\mathscr{S}$ . We study this quantity for two-dimensional spaces of operators and for single generated algebras and their commutants.
Keywords:	mathematics, operator theory, reflexivity defect, reflexivity, two-dimensional space of operators, single generated algebra, commutant
Year of publishing:	2009
Number of pages:	str. 344-359
Numbering:	Vol. 430, iss. 1
PID:	20.500.12556/RUP-7728
ISSN:	0024-3795
UDC:	517.983:512.643
DOI:	10.1016/j.laa.2008.07.024
COBISS.SI-ID:	14977369
Publication date in RUP:	03.04.2017
Views:	2754
Downloads:	196
Metadata:
:	BRAČIČ, Janko and KUZMA, Bojan, 2009, Reflexivity defect of spaces of linear operators. [online]. 2009. Vol. 430, no. 1, p. 344–359. [Accessed 5 April 2025]. DOI 10.1016/j.laa.2008.07.024. Retrieved from: http://dx.doi.org/10.1016/j.laa.2008.07.024 Copy citation

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Language:	Slovenian
Title:	Refleksivnostni defekt prostorov linearnih operatorjev
Abstract:	Za končnodimenzionalen linearen prostor ${\mathscr{S}} \subseteq {\mathscr{L}} (V,W)$ in naravno število $k$ je $k$ -refleksivnostni defekt prostora ${\mathscr{S}}$ definiran kot ${\mathrm{rd}}_k ({\mathscr{S}}) = \dim({\mathrm{Ref}}_k (\mathscr{S})/\mathscr{S})$ , pri čemer je ${\mathrm{Ref}}_k$ $k$ -refleksivnostno zaprtje za $\mathscr{S}$ . V članku izračunamo refleksivnostni defekt za dvodimenzionalne prostore operatorjev, za algebre generirane z enim operatorjem in za njihove komutante.
Keywords:	matematika, teorija operatorjev, refleksivnost, refleksivnostni defekt, dvodimenzionalen prostor operatorjev, algebra generirana z enim operatorjem, komutant

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