Abstract
In this paper, we discuss measure theoretic characterizations for Lambert conditional operators in some operator classes on \(L^2(\Sigma )\) such as, p-hyponormal, centered, n-normal and binormal. In addition, it is showed when these operators are orthogonal projection and some correlations between these types of operators are established.
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Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, Berlin (2003)
Djordjević, D.S., Dinčić, N.C.: Reverse order law for the Moore–Penrose inverse. J. Math. Anal. Appl. 361, 252–261 (2010)
Dodds, P., Huijsmans, C., de Pagter, B.: Characterizations of conditional expectation-type operators. Pac. J. Math. 141, 55–77 (1990)
Douglas, R.G.: Contractive projections on an \(L_1\) space. Pac. J. Math. 15, 443–462 (1965)
Estaremi, Y., Jabbarzadeh, M.R.: Weighted Lambert conditionaltype operators on \(L^p\) spaces. Oper. Matrices 7, 101–116 (2013)
Furuta, T.: Invitation to Linear Operators. Taylor & Francis Ltd, London (2001)
Grobler, J.J., de Pagter, B.: Operators representable as multiplication conditional expectation operators. J. Oper. Theory 48, 15–40 (2002)
Herron, J.: Weighted conditional expectation operators on \(L^p\) spaces, UNC Charlotte Doctoral Dissertation (2004)
Herron, J.: Weighted conditional expectation operators. Oper. Matrices 5, 107–118 (2011)
Jabbarzadeh, M.R., Jafari Bakhshkandi, M.: Centered operators via Moore–Penrose inverse and Aluthge transformations. Filomat 31, 6441–6448 (2017)
Jabbarzadeh, M.R., Sohrabi Chegeni, M.: Moore–Penrose inverse of conditional type operators. Oper. Matrices 11, 289–299 (2017)
Jabbarzadeh, M.R., Sharifi, M.H.: Lambert conditional type operators on \(L^2(\Sigma )\). Linear Multilinear Algebra 67, 2030–2047 (2019)
Jabbarzadeh, M.R., Sharifi, M.H.: Operators whose ranges are contained in the null space of conditional expectations. Math. Nachr. 292, 2427–2440 (2019)
Lambert, A.: \(L^p\) multipliers and nested sigma-algebras. Oper. Theory Adv. Appl. 104, 147–153 (1998)
Lambert, A.: Localising sets for sigma-algebras and related point transformations. Proc. Royal Soc. Edinburgh 118A, 111–118 (1991)
Lambert, A., Weinstock, B.M.: A class of operator algebras induced by probabilistic conditional expectations. Michigan Math. J. 40, 359–376 (1993)
Morrel, B.B., Muhly, P.S.: Centered operators. Studia Math. 51, 251–263 (1974)
Moy, S.-T.C.: Characterizations of conditional expectation as a transformation on function spaces. Pac. J. Math. 4, 47–63 (1954)
Patel, S.: A note on quasi-isometries. Glas. Mat. 35, 307–312 (2000)
Rao, M.M.: Conditional Measure and Applications. Marcel Dekker, New York (1993)
Yamazaki, T.: On the polar decomposition of the Aluthge transformation and related results. J. Oper. Theory 51, 303–319 (2004)
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The authors are very grateful to the referee(s) for careful reading of the paper and for a number of helpful comments and corrections which improved the presentation of this paper.
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Communicated by Sanne ter Horst, Dmitry S. Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.
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Emamalipour, H., Jabbarzadeh, M.R. Lambert Conditional Operators on \(L^2(\Sigma )\). Complex Anal. Oper. Theory 14, 18 (2020). https://doi.org/10.1007/s11785-020-00982-8
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DOI: https://doi.org/10.1007/s11785-020-00982-8