Spectrum of weighted composition operators part IV spectrum and essential spectra of weighted composition operators in spaces of smooth functions on [0, 1]
We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in spaces C ( n ) [ 0 , 1 ] and Sobolev spaces W n , X = { f ∈ C ( n - 1 ) [ 0 , 1 ] : f ( n ) ∈ X } where X is an interpolation space between L 1 [ 0 , 1 ] and L ∞ [ 0 , 1 ] .
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| Vydáno v: | Positivity : an international journal devoted to the theory and applications of positivity in analysis Ročník 21; číslo 3; s. 989 - 1014 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.09.2017
Springer Nature B.V |
| Témata: | |
| ISSN: | 1385-1292, 1572-9281 |
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| Abstract | We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in spaces
C
(
n
)
[
0
,
1
]
and Sobolev spaces
W
n
,
X
=
{
f
∈
C
(
n
-
1
)
[
0
,
1
]
:
f
(
n
)
∈
X
}
where
X
is an interpolation space between
L
1
[
0
,
1
]
and
L
∞
[
0
,
1
]
. |
|---|---|
| AbstractList | (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in spaces ... and Sobolev spaces ... where X is an interpolation space between ... and ... We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in spaces C ( n ) [ 0 , 1 ] and Sobolev spaces W n , X = { f ∈ C ( n - 1 ) [ 0 , 1 ] : f ( n ) ∈ X } where X is an interpolation space between L 1 [ 0 , 1 ] and L ∞ [ 0 , 1 ] . |
| Author | Kitover, A. K. |
| Author_xml | – sequence: 1 givenname: A. K. orcidid: 0000-0002-1996-8201 surname: Kitover fullname: Kitover, A. K. email: akitover@ccp.edu organization: Community College of Philadelphia |
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| Cites_doi | 10.2307/2695352 10.1016/0022-1236(69)90014-7 10.1007/s11117-012-0196-2 10.1007/s11117-010-0106-4 10.1017/CBO9780511618864 |
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| DOI | 10.1007/s11117-016-0448-7 |
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| Keywords | Fredholm spectrum Disjointness preserving operators Secondary 47B48 Primary 47B33 46B60 Essential spectra Spectrum |
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| References | EdmundsDEEvansWDSpectral Theory and Differential Operators1987OxfordClarendon Press0628.47017 KamowitzHScheinbergSThe spectrum of automorphisms of Banach algebrasJ. Funct. Anal.1969426827625007510.1016/0022-1236(69)90014-70182.17703 Walker R.C.: The Stone–C̆ech Compactification, Ergebnisse der Mathematics und ihrer Grenzgebiete, vol. 83. Springer, New York (1974) JohnsonWPThe Curious History of Faà di Bruno’s FormulaAm. Math. Mon.2002109321723410.2307/26953521024.01010 Kitover A.K.: Spectrum of Weighted Composition Operators. Part III. Essential spectra of some disjointness preserving operators on Banach lattices. In: Ordered Structures and Applications: Positivity VII Trends in Mathematics, 233261, Springer International Publishing, Berlin (2016). arXiv:1309.4475v1 [math.SP] 17 Sep 2013 Krein S.G., Petunin Y.I., Semenov E.M.: Interpolation of Linear Operators, Translation of Mathematical Monographs, vol. 54. AMS, Providence (1982) BennettCSharpleyRInterpolation of Operators1988BostonAcademic Press0647.46057 Davies E.B. Linear opeartors and their Spectra. Cambridge Studies in Advanced Mathematics, vol. 106. Cambridge University Press, Cambridge (2007) KantorovichLVAkilovGPFunctional Analysis1982OxfordPergamon Press0484.46003 MüllerVSpectral Theory of Linear Operators2007BaselBirkhäuser1208.47001 KitoverAKSpectrum of weighted composition operators. Part II. Weihgted composition operators on subspaces of Banach latticesPositivity201317655676309068510.1007/s11117-012-0196-21288.47027 KitoverAKSpectrum of weighted composition operators: part 1. Weighted composition operators on C(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C(K)$$\end{document} and uniform algebrasPositivity2011154639659286160310.1007/s11117-010-0106-41284.47023 Abramovich Y.A., Arenson E.L., Kitover A.K.: Banach C(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C(K)$$\end{document}-Modules and Operators Preserving Disjointness, Pitman Research Notes in Mathematical Series, vol. 277. Longman, Harlow (1997) H Kamowitz (448_CR6) 1969; 4 C Bennett (448_CR2) 1988 WP Johnson (448_CR5) 2002; 109 AK Kitover (448_CR9) 2013; 17 LV Kantorovich (448_CR7) 1982 AK Kitover (448_CR8) 2011; 15 V Müller (448_CR12) 2007 448_CR13 448_CR1 448_CR3 448_CR11 DE Edmunds (448_CR4) 1987 448_CR10 |
| References_xml | – reference: EdmundsDEEvansWDSpectral Theory and Differential Operators1987OxfordClarendon Press0628.47017 – reference: Abramovich Y.A., Arenson E.L., Kitover A.K.: Banach C(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C(K)$$\end{document}-Modules and Operators Preserving Disjointness, Pitman Research Notes in Mathematical Series, vol. 277. Longman, Harlow (1997) – reference: BennettCSharpleyRInterpolation of Operators1988BostonAcademic Press0647.46057 – reference: Davies E.B. Linear opeartors and their Spectra. Cambridge Studies in Advanced Mathematics, vol. 106. Cambridge University Press, Cambridge (2007) – reference: Kitover A.K.: Spectrum of Weighted Composition Operators. Part III. Essential spectra of some disjointness preserving operators on Banach lattices. In: Ordered Structures and Applications: Positivity VII Trends in Mathematics, 233261, Springer International Publishing, Berlin (2016). arXiv:1309.4475v1 [math.SP] 17 Sep 2013 – reference: MüllerVSpectral Theory of Linear Operators2007BaselBirkhäuser1208.47001 – reference: JohnsonWPThe Curious History of Faà di Bruno’s FormulaAm. Math. Mon.2002109321723410.2307/26953521024.01010 – reference: KamowitzHScheinbergSThe spectrum of automorphisms of Banach algebrasJ. Funct. Anal.1969426827625007510.1016/0022-1236(69)90014-70182.17703 – reference: Krein S.G., Petunin Y.I., Semenov E.M.: Interpolation of Linear Operators, Translation of Mathematical Monographs, vol. 54. AMS, Providence (1982) – reference: KitoverAKSpectrum of weighted composition operators: part 1. Weighted composition operators on C(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C(K)$$\end{document} and uniform algebrasPositivity2011154639659286160310.1007/s11117-010-0106-41284.47023 – reference: KantorovichLVAkilovGPFunctional Analysis1982OxfordPergamon Press0484.46003 – reference: Walker R.C.: The Stone–C̆ech Compactification, Ergebnisse der Mathematics und ihrer Grenzgebiete, vol. 83. Springer, New York (1974) – reference: KitoverAKSpectrum of weighted composition operators. Part II. Weihgted composition operators on subspaces of Banach latticesPositivity201317655676309068510.1007/s11117-012-0196-21288.47027 – volume: 109 start-page: 217 issue: 3 year: 2002 ident: 448_CR5 publication-title: Am. Math. Mon. doi: 10.2307/2695352 – volume: 4 start-page: 268 year: 1969 ident: 448_CR6 publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(69)90014-7 – volume-title: Interpolation of Operators year: 1988 ident: 448_CR2 – volume-title: Spectral Theory and Differential Operators year: 1987 ident: 448_CR4 – volume: 17 start-page: 655 year: 2013 ident: 448_CR9 publication-title: Positivity doi: 10.1007/s11117-012-0196-2 – ident: 448_CR1 – volume: 15 start-page: 639 issue: 4 year: 2011 ident: 448_CR8 publication-title: Positivity doi: 10.1007/s11117-010-0106-4 – volume-title: Spectral Theory of Linear Operators year: 2007 ident: 448_CR12 – ident: 448_CR10 – volume-title: Functional Analysis year: 1982 ident: 448_CR7 – ident: 448_CR3 doi: 10.1017/CBO9780511618864 – ident: 448_CR11 – ident: 448_CR13 |
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n
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[
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,
1
]
and Sobolev... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) We provide a description of the spectrum and essential spectra of invertible... |
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| SubjectTerms | Calculus of Variations and Optimal Control; Optimization Econometrics Fourier Analysis Interpolation Mathematics Mathematics and Statistics Operator Theory Operators (mathematics) Potential Theory Sobolev space |
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| Title | Spectrum of weighted composition operators part IV spectrum and essential spectra of weighted composition operators in spaces of smooth functions on [0, 1] |
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