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Abstrakty
In this paper, we discuss some properties of the weighted Hankel operator H(...) and describe the conditions on which the weighted Hankel operator H(...) and weighted Toeplitz operator T(...), with (…) on the space H(...) being a sequence of positive numbers with (…), commute. It is also proved that if a non-zero weighted Hankel operator H(...) commutes with T(...), which is not a multiple of the identity, then H(...), for some (…).
Wydawca
Czasopismo
Rocznik
Tom
Strony
571--583
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Department of Mathematics, PGDAV College, University of Delhi, Delhi - 110065, India
autor
- Department of Mathematics, PGDAV College, University of Delhi, Delhi - 110065, India
Bibliografia
- [1] A. Brown, P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1964), 89–102.
- [2] G. Datt, D. K. Porwal, Weighted Hankel operators, Jr. Adv. Res. Pure Math. 5(2) (2013), 59–70.
- [3] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, 1967.
- [4] M. C. Ho, Properties of slant Toeplitz operators, Indiana Univ. Math. J. 45 (1996), 843–862.
- [5] V. Lauric, On a weighted Toeplitz operator and its commutant, Int. J. Math. Math. Sci. 6 (2005), 823–835.
- [6] R. A. Martinez Avendano, Hankel operators and generalizations, Ph.D Thesis, University of Toronto, 2000.
- [7] Z. Nehari, On bounded bilinear forms, Ann. of Math. 65 (1957), 153–162.
- [8] S. C. Power, Hankel operators on Hilbert space, Bull. London Math. Soc. 12 (1980), 422–442.
- [9] D. Sarason, On product of Toeplitz operators, Acta. Sci. Math. (Szeged) 35 (1973), 7–12.
- [10] D. Sarason, Holomorphic spaces: a brief and selective survey, in: Holomorphic Spaces, 1–34, Math. Sci. Res. Inst. Publ. 33, Cambridge Univ. Press, Cambridge, 1998.
- [11] A. L. Shields, Weighted shift operators and analytic function theory, in Topics in Operator Theory , Math. Surveys, No. 13, American Mathematical Society, Rhode Ireland, (1974), 49–128.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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