Abstract
Let \(L^2(\mu )\) denote the separable Hilbert space associated with a \(\sigma \)-finite atomic measure \(\mu \). In this paper, we determine necessary and sufficient conditions for boundedness of weighted composition transformation on \(L^2(\mu )\) and give a characterization of antinormal weighted composition operators on \(L^2(\mu )\).
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References
Abramovich, Y.A.; Aliprantis, C.D.: An Invitation to Operator Theory, Graduate Studies in Mathematics, American Mathematical Society, Providence (2002)
Conway, J.B.: A Course in Functional Analysis, 2nd edn. Springer, Berlin (1990)
ter Elst, A.F.M.: Antinormal operators. Acta. Sci. Math. 54, 151–158 (1990)
Fan, K.; Hoffman, A.: Some metric inequalities in the space of matrices. Proc. Am. Math. Soc. 6, 111–116 (1955)
Fujii, M.; Nakamoto, R.: Antinormal operators and theorems of Izumino. Math. Jpn. 24, 41–44 (1979)
Halmos, P.R.: Positive approximants of operators. Indiana Univ. Math. J. 21, 951–960 (1972)
Holmes, R.B.: Best approximation by normal operators. J. Approx. Theory 12, 412–417 (1974)
Holmes, R.B.; Kripke, B.R.: Best approximation by compact operators. Ind. Univ. Math. J. 21, 255–263 (1971)
Izumino, S.: Inequalities on normal and antinormal operators. Math. Jpn. 23, 211–215 (1978)
Izumino, S.: Inequalities on nilpotent operators. Math. Jpn. 24, 31–34 (1979)
Kumar, D.; Chandra, H.: Composition operators on Poisson weighted sequence spaces. Funct. Anal. Approx. Comput. 8(1), 21–37 (2016)
Kumar, D.; Chandra, H.: Antinormal composition operators on \(l^{2}(\lambda )\). Mat. Vesn. 68(4), 259–266 (2016)
Rogers, D.D.: On proximal sets of normal operators. Proc. Am. Math. Soc. 61, 44–48 (1976)
Singh, R.K.; Manhas, J.S.: Composition Operators on Function Spaces. North-Holland, New York (1993)
Tripathi, G.P.; Lal, N.: Antinormal composition operators on \(l^2\). Tamkang J. Math. 39, 347–352 (2008)
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Kumar, D., Chandra, H. Antinormal weighted composition operators on \(L^2(\mu )-\)space of an atomic measure space. Arab. J. Math. 9, 137–143 (2020). https://doi.org/10.1007/s40065-018-0228-2
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DOI: https://doi.org/10.1007/s40065-018-0228-2