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## Multivariate analogue of slant Toeplitz operators

#### Gopal DATT [1] , Shesh PANDEY [2]

This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on the Lebesgue space of the $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ and $n\geq 1$. We obtain certain equivalent conditions for the commutativity and essential commutativity of these operators. In the last section, we deal with the spectrum of a $k^{th}$-order slant Toeplitz operator on $L^2(\mathbb{T}^n)$ and investigate the conditions for such an operator to be an isometry, hyponormal or normal.
commutativity, Lebesgue space, slant Toeplitz operators, n-dimensional torus
• [1] S.C. Arora and R. Batra, Generalized slant Toeplitz operators on $H^2$, Math. Nachr. 278 (4), 347-355, 2005.
• [2] G. Datt and N. Ohri, Properties of slant Toeplitz operators on the torus, Malays. J. Math. Sci. 12, (2), 195-206, 2018.
• [3] G. Datt and S.K. Pandey, Slant Toeplitz operators on Lebesgue space of n-dimensional Torus, Hokkaido Math. J. 49 (3), 363-389, 2020.
• [4] X. Ding, S. Sun and D. Zheng, Commuting Toeplitz operators on the bidisk, J. Funct. Anal. 263, 3333-3357, 2012.
• [5] C. Gu and D. Zheng, The semi-commutator of Toeplitz operators on the bidisc, J. Operator Theory 38, 173-193, 1997.
• [6] H. Guediri, Dual Toeplitz operators on the sphere, Acta Math. Sin. (Engl. Ser.) 19 (9), 1791-1808, 2013.
• [7] M.C. Ho, Spectral properties of slant Toeplitz operators, Ph.D. thesis, Purdue- University, Indiana, 1996.
• [8] M.C. Ho, Spectra of slant Toeplitz operators with continuous symbol, Michigan Math. J. 44, 157-166, 1997.
• [9] Y.F. Lu and B. Zhang, Commuting Hankel and Toeplitz operators on the Hardy space of the bidisk, J. Math. Res. Exposition 30 (2), 205-216, 2010.
• [10] V. Peller, Hankel operators and applications, Springer-Verlag, New York, 2003.
• [11] W. Rudin, Function Theory in Polydisc, W.A. Benjamin Inc., New York-Amsterdam 1969.
• [12] E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971.
Primary Language en Mathematics Mathematics Orcid: 0000-0001-6513-4411Author: Gopal DATT (Primary Author)Institution: University of DelhiCountry: India Orcid: 0000-0001-9121-8838Author: Shesh PANDEYInstitution: University of DelhiCountry: India Publication Date : June 7, 2021
 Bibtex @research article { hujms663262, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {678 - 691}, doi = {10.15672/hujms.663262}, title = {Multivariate analogue of slant Toeplitz operators}, key = {cite}, author = {Datt, Gopal and Pandey, Shesh} } APA Datt, G , Pandey, S . (2021). Multivariate analogue of slant Toeplitz operators . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 678-691 . DOI: 10.15672/hujms.663262 MLA Datt, G , Pandey, S . "Multivariate analogue of slant Toeplitz operators" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 678-691 Chicago Datt, G , Pandey, S . "Multivariate analogue of slant Toeplitz operators". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 678-691 RIS TY - JOUR T1 - Multivariate analogue of slant Toeplitz operators AU - Gopal Datt , Shesh Pandey Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.663262 DO - 10.15672/hujms.663262 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 678 EP - 691 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.663262 UR - https://doi.org/10.15672/hujms.663262 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Multivariate analogue of slant Toeplitz operators %A Gopal Datt , Shesh Pandey %T Multivariate analogue of slant Toeplitz operators %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.663262 %U 10.15672/hujms.663262 ISNAD Datt, Gopal , Pandey, Shesh . "Multivariate analogue of slant Toeplitz operators". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 678-691 . https://doi.org/10.15672/hujms.663262 AMA Datt G , Pandey S . Multivariate analogue of slant Toeplitz operators. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 678-691. Vancouver Datt G , Pandey S . Multivariate analogue of slant Toeplitz operators. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 678-691. IEEE G. Datt and S. Pandey , "Multivariate analogue of slant Toeplitz operators", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 678-691, Jun. 2021, doi:10.15672/hujms.663262

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