Abstract
With the present paper, we attempt to describe the unbounded generalized multiplication operators, induced by some specific symbols, defined on the weighted Hardy spaces. We study their densely defined behavior and closedness together with the discussion of their normality and self-adjointness.
Similar content being viewed by others
References
R. A. M. Avendaño and P. Rosenthal, An Introduction to Operators on the Hardy-Hilbert space (Springer, 2007).
M. B. Abrahamse, Multiplication Operators, Lecture Notes in Mathematics (Springer, Berlin, Heidelberg, 1938).
S. C. Arora, G. Datt, and S. Verma, “Multiplication operators on Lorentz spaces,” Indian J. Math. 48, 317–329 (2006).
G. Datt and M. Jain, “Generalized multiplication operators of higher order on weighted Hardy spaces,” Asian European Journal of Mathematics (in press). https://doi.org/10.1142/S1793557120501028
S. Goldberg, Unbounded Linear Operators: Theory and Applications (Dover, New York, 2006).
K. Guo, S. Sun, D. Zheng, and C. Zhong, “Multiplication operators on the Bergman space via the Hardy space of the bidisk,” J. Reine Angew. Math. 628 (2009).
P. R. Halmos, A Hilbert Space Problem Book (Van Nostrand, Princeton, NJ, 1967).
Z. J. Jablonski, B. Jung II, and J. Stochel, “Unbounded quasinormal operators revisited,” Integr. Equat. Oper. Theory 79, 135–149 (2014).
R. L. Kelley, “Weighted shifts on Hilbert space,” Dissertation (Univ. of Michigan, Ann Arbor, MI, 1966).
B. S. Komal and S. Gupta, “Multiplication operators between Orlicz spaces,” Dissertationes Math. (Rozprawy Mat.) 41, 324–330 (2001).
E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, Chichester, 1978).
V. Lauric, “On a weighted Toepliz operator and its commutant,” Int. J. Math. Math. Sci. 6, 823–835 (2005).
S. K. Sharma and B. S. Komal, “Generalized multiplication operators on weighted Hardy spaces,” Lobachevskii J. Math. 32, 298–303 (2011).
W. Rudin, Functional Analysis, 2nd ed. (McGraw Hill Education, India, 2006).
S. K. Sharma and B. S. Komal, “Multiplication operators on weighted Hardy spaces,” Lobachevskii J. Math. 33, 165–169 (2012).
A. L. Shields, Weighted Shift Operators and Analytic Function Theory, Vol. 13 of Topics in Operator Theory, Math. Surveys (Am. Math. Soc., Providence, RI, 1974).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by E. K. Lipachev)
Rights and permissions
About this article
Cite this article
Datt, G., Jain, M. & Ohri, N. A Note on Unbounded Generalized Multiplication Operators. Lobachevskii J Math 40, 166–173 (2019). https://doi.org/10.1134/S1995080219020070
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080219020070