Some classes of weighted conditional type operators and their spectra

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• 作者：Y. Estaremi (1)
  
  1. Department of mathematics ; Payame Noor university ; P. O. Box ; 19395-3697 ; Tehran ; Iran
  
• 关键词：Conditional expectation ; $$A$$ A ; class ; $$*$$ 鈭 ; $$A$$ A ; class ; Polar decomposition ; Aluthage transformation ; Spectrum ; Point spectrum ; Spectral radius ; 47B47
• 刊名：Positivity
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：19
• 期：1
• 页码：83-93
• 全文大小：183 KB
• 参考文献：1. De Pagter, B.: \(f\) - algebras and orthomorphisms, thesis, Leiden University (1981)
  2. Dodds, PG, Huijsmans, CB, Pagter, B (1990) characterizations of conditional expectation-type operators. Pacific J. Math. 141: pp. 55-77 CrossRef
  3. Estaremi, Y.: Essential norm of weighted conditional type operators on \(L^p\) -spaces. Positivity
  4. Estaremi, Y, Jabbarzadeh, MR (2013) Weighted lambert type operators on $$L^{p}$$ L p -spaces. Oper. Matrices 1: pp. 101-116 CrossRef
  5. Furuta, T (2001) Invitation to Linear Operators. Taylor and Francis, London CrossRef
  6. Grobler, JJ, Pagter, B (2002) Operators representable as multiplication-conditional expectation operators. J. Oper. Theory 48: pp. 15-40
  7. Herron, J (2011) Weighted conditional expectation operators. Oper. Matrices 1: pp. 107-118 CrossRef
  8. Lambert, A (1998) $$L^p$$ L p multipliers and nested sigma-algebras. Oper. Theory Adv. Appl. 104: pp. 147-153
  9. Lambert, A., Weinstock, B.M.: A class of operator algebras induced by probabilistic conditional expectations. Michigan Math. J. 40, 359鈥?76 (1993)
  10. Moy, S.T.C.: Characterizations of conditional expectation as a transformation on function spaces. Pacific J. Math. 4, 47鈥?3 (1954)
  11. Rao, MM (1993) Conditional measure and applications. Marcel Dekker, New York
  12. Yamazaki, T (2001) An expression of spectral radius via Aluthge transformation. Proc. AMS 4: pp. 1131-1137
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Operator Theory
  Potential Theory
  Calculus of Variations and Optimal Control
  Econometrics
  
• 出版者：Birkh盲user Basel
• ISSN：1572-9281

文摘

In this paper, some \(*\) -classes of weighted conditional expectation type operators, such as \(A\) -class, \(*\) - \(A\) -class and quasi- \(*\) - \(A\) classes on \(L^{2}(\Sigma )\) are investigated. Also, the spectrum, point spectrum and spectral radius of these operators are computed.