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論文名稱 Title |
半單調巴赫納代數上的區部自同構算子 Local automorphism of semisimple Banach algebras |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
18 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2006-06-16 |
繳交日期 Date of Submission |
2006-06-26 |
關鍵字 Keywords |
局部自同構算子 local automorphism, socle |
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統計 Statistics |
本論文已被瀏覽 5705 次,被下載 2036 次 The thesis/dissertation has been browsed 5705 times, has been downloaded 2036 times. |
中文摘要 |
一個從代數A映射到代數A本身的算子θ,算子θ本身不一定具備有線性,連續性和乘法跟映射的可交換性。如果算子θ作用在代數空間A上的每個點a,都可以找到一個代數空間A的自同構映射算子θa,使得滿足θ(a)=θa(a)。那麼算子θ就被叫做代數A的區部自同構算子。在此篇論文中,我們討論的問題是在什麼樣的情況下,作用在半單調巴納赫代數的局部自同構算子會是喬登同構算子。並且在此篇論文中,代數不一定擁有乘法單位元,但是擁有乘法結合律。 |
Abstract |
A not necessarily continuous, linear or multiplicative function θ from an algebra A into itself is called a local automorphism if θ agrees with an automorphism of A at each point in $A$. In this paper, we study the question when a local automorphism of a semisimple Banach algebra, is a Jordan isomorphism. Also a algebra is not necessary unital, but be implicitly assumed to be associative. |
目次 Table of Contents |
1.Introduction 1 2.Preliminary 3 3.Conclusion and Main Result 8 |
參考文獻 References |
A. R. Sourour, "Invertibility preservinf linear maps on {L}(X), Trans. Amer. Math. Soc},348 (1996), no. 1}, 13--30 B. Aupetlt and H. du T. Mouton. "Spectrum preserving linear mappings in Banach algebras". Studia Math. {109} (1994), 91--100. B. Aupetit, "Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras", J. London Math. Soc, {62} (2000), 917--924. M. Bres}ar and P. Semrl, "Mappings wich preserve idempoyents, local automorphism, and local derivations", Can. J. Math}. { 45} (1993), { no.3}, 483-496. M. Bresar and P. Semrl, "Invertibility preserving maps reserve idempotents", Michigan Math. J, {45} (1998), 483--488. M. Bresar and P. Semrl, "Spectral characterization of idempotents and invertibility preserving linear maps", Expostiones Math. {17,} (1999), 185--192. M. Bres}ar and P. Semrl, "Finite ranh elements in smisimple Banach algebras", Studia Math. {128} (1998), 287--298. M. D. Choi, D. Hadwin, E. Nordgren, H. Radjavi and P. Rosenthal, "On positive linear maps preserving invertibility", J. Funct. Anal}, {59} (1984), { no. 3}, 462--469. I. N.Herstein, "Topic in ring theory", University of Chicago, (1969). Jung-Hui Liu, Ngai-Ching wong and Jen-chih YAo. "Local automorphisms of operator algebras". submitted to Linear Algebra and its Applications. David R.~Larson. "A note on invertibility preservers on Banach algebras", Proc. Amer. Math. Soc. {131, no. 12} (2003), 3833--3837. Kenneth R. Davidson C*-algebra by example", M. Mathieu. "Spectally bounded operators on simple C*-algebra", Proc. Amer. Math. Soc. { 132, no. 2} (2003), 443--446. T. Mouton and H. Raubenheimer. "On rank one and finite elements og Banach algebras", Studia Math. { 104} (1993), 211--219. M. Omladi$check{}{c}$ and P. S}emrl,, "Linear mappings that preserve potent operators", Proc. Amer. Math. Soc. { 123, no. 6} (1995), 1851--1855. P. Semal, "Invertibility preserving linear maps and algebraic reflexivity of elementary operators of length one", Proc. Amer. Math. Soc. { 130, no. 3} (2001), 769--772. Theodore W. Palmer, "Banach algebras and the general theory of C*-algebras ", Cambridge [England] ; New York, NY, USA : Cambridge University Press, (1994) --, "A primer on spectral theory", Springer, Be rlin, (1991). |
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