Geodesic
Slant Hankel operators
Archivum mathematicum, Tome 42 (2006) no. 2, pp. 125-133 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper the notion of slant Hankel operator $K_\varphi$, with symbol $\varphi$ in $L^\infty$, on the space $L^2({\Bbb T})$, ${\Bbb T}$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis $\{z^i : i \in {\Bbb Z} \}$ of the space $L^2$ is given by $\langle\alpha_{ij}\rangle = \langle a_{-2i-j}\rangle$, where $\sum\limits_{i=-\infty}^{\infty}a_i z^i$ is the Fourier expansion of $\varphi$. Some algebraic properties such as the norm, compactness of the operator $K_\varphi$ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible symbol $\varphi$, the spectrum of $K_\varphi$ contains a closed disc.
In this paper the notion of slant Hankel operator $K_\varphi$, with symbol $\varphi$ in $L^\infty$, on the space $L^2({\Bbb T})$, ${\Bbb T}$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis $\{z^i : i \in {\Bbb Z} \}$ of the space $L^2$ is given by $\langle\alpha_{ij}\rangle = \langle a_{-2i-j}\rangle$, where $\sum\limits_{i=-\infty}^{\infty}a_i z^i$ is the Fourier expansion of $\varphi$. Some algebraic properties such as the norm, compactness of the operator $K_\varphi$ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible symbol $\varphi$, the spectrum of $K_\varphi$ contains a closed disc.
Classification : 47A10, 47B35
Keywords: Hankel operators; slant Hankel operators; slant Toeplitz operators 
@article{ARM_2006_42_2_a2,
     author = {Arora, S. C. and Batra, Ruchika and Singh, M. P.},
     title = {Slant {Hankel} operators},
     journal = {Archivum mathematicum},
     pages = {125--133},
     year = {2006},
     volume = {42},
     number = {2},
     mrnumber = {2240189},
     zbl = {1164.47325},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a2/}
}
TY  - JOUR
AU  - Arora, S. C.
AU  - Batra, Ruchika
AU  - Singh, M. P.
TI  - Slant Hankel operators
JO  - Archivum mathematicum
PY  - 2006
SP  - 125
EP  - 133
VL  - 42
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a2/
LA  - en
ID  - ARM_2006_42_2_a2
ER  - 
%0 Journal Article
%A Arora, S. C.
%A Batra, Ruchika
%A Singh, M. P.
%T Slant Hankel operators
%J Archivum mathematicum
%D 2006
%P 125-133
%V 42
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a2/
%G en
%F ARM_2006_42_2_a2
Arora, S. C.; Batra, Ruchika; Singh, M. P. Slant Hankel operators. Archivum mathematicum, Tome 42 (2006) no. 2, pp. 125-133. http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a2/

[1] Arora S. C., Ruchika Batra: On Slant Hankel Operators. to appear in Bull. Calcutta Math. Soc. | MR

[2] Brown A., Halmos P. R.: Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213 (1964), 89–102. | MR

[3] Halmos P. R.: Hilbert Space Problem Book. Springer Verlag, New York, Heidelberg-Berlin, 1979.

[4] Ho M. C.: Properties of Slant Toeplitz operators. Indiana Univ. Math. J. 45 (1996), 843–862. | MR | Zbl