The notion of an essentially slant Toeplitz operator on the space $L^2$ is introduced and some of the properties of the set ${\rm ESTO}(L^2)$, the set of all essentially slant Toeplitz operators on $L^2$, are investigated. In particular the conditions under which the product of two operators in ${\rm ESTO}(L^2)$ is in ${\rm ESTO}(L^2)$ are discussed. The notion is generalized to $k$th-order essentially slant Toeplitz operators.
References
M.B. Abrahamse, Toeplitz operators in multiply connected domain, Bull. Amer. Math. Soc. 77 (1971),449--454. MR273435 0212.16001 10.1090/S0002-9904-1971-12734-9 euclid.bams/1183532831
M.B. Abrahamse, Toeplitz operators in multiply connected domain, Bull. Amer. Math. Soc. 77 (1971),449--454. MR273435 0212.16001 10.1090/S0002-9904-1971-12734-9 euclid.bams/1183532831
S.C. Arora and R. Batra, On generalized slant Toeplitz operators, Indian Journal of Mathematics 45 (2) (2003), 121--134. MR2035900 1067.47038S.C. Arora and R. Batra, On generalized slant Toeplitz operators, Indian Journal of Mathematics 45 (2) (2003), 121--134. MR2035900 1067.47038
J. Barria and P.R. Halmos, Asymptotic Toeplitz Operators, Trans. Amer. Math. Soc. 273 (1982), 621--630. MR667164 0522.47020 10.2307/1999932J. Barria and P.R. Halmos, Asymptotic Toeplitz Operators, Trans. Amer. Math. Soc. 273 (1982), 621--630. MR667164 0522.47020 10.2307/1999932
A. Devinatz, Toeplitz operator on $H^2$ space, Trans. Amer. Math. Soc. 112 (1964), 304--317. MR163174 0139.07202 10.2307/1994297A. Devinatz, Toeplitz operator on $H^2$ space, Trans. Amer. Math. Soc. 112 (1964), 304--317. MR163174 0139.07202 10.2307/1994297
T. Goodman, C.Micchelli and J.Ward, Spectral radius formula for subdivision operators, Recent Advances in Wavelet Analysis, ed. L. Schumaker and G. Webb, Academic Press, (1994), 335--360. MR1244611 0840.42020T. Goodman, C.Micchelli and J.Ward, Spectral radius formula for subdivision operators, Recent Advances in Wavelet Analysis, ed. L. Schumaker and G. Webb, Academic Press, (1994), 335--360. MR1244611 0840.42020
M.C. Ho, Properties of slant Toeplitz operators, Indiana Univ. Math. J. 45 (1996), 843--862. MR1422109 0880.47016 10.1512/iumj.1996.45.1973M.C. Ho, Properties of slant Toeplitz operators, Indiana Univ. Math. J. 45 (1996), 843--862. MR1422109 0880.47016 10.1512/iumj.1996.45.1973
O. Toeplitz, Zur theorie der quadratischen und bilinearan Formen von unendlichvielen, Veranderlichen, Math. Ann. 70 (1911), 351--376. MR1511625 10.1007/BF01564502O. Toeplitz, Zur theorie der quadratischen und bilinearan Formen von unendlichvielen, Veranderlichen, Math. Ann. 70 (1911), 351--376. MR1511625 10.1007/BF01564502
L. Villemoes, Wavelet analysis of refinement equations, SIAM J. Math. Analysis 25 (1994), 1433--1460. MR1289147 0809.42016 10.1137/S0036141092228179L. Villemoes, Wavelet analysis of refinement equations, SIAM J. Math. Analysis 25 (1994), 1433--1460. MR1289147 0809.42016 10.1137/S0036141092228179
T. Zegeye and S.C. Arora, The compression of a slant Toeplitz operator to $H^2$, Indian J. Pure Appl. Math. 32 (2) (2001), 221--226. MR1820862 0988.47015T. Zegeye and S.C. Arora, The compression of a slant Toeplitz operator to $H^2$, Indian J. Pure Appl. Math. 32 (2) (2001), 221--226. MR1820862 0988.47015