| Title:
|
Slant Hankel operators (English) |
| Author:
|
Arora, S. C. |
| Author:
|
Batra, Ruchika |
| Author:
|
Singh, M. P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
125-133 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hankel operators |
| Keyword:
|
slant Hankel operators |
| Keyword:
|
slant Toeplitz operators |
| MSC:
|
47A10 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 1164.47325 |
| idMR:
|
MR2240189 |
| . |
| Date available:
|
2008-06-06T22:47:36Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107988 |
| . |
| Reference:
|
[1] Arora S. C., Ruchika Batra: On Slant Hankel Operators.to appear in Bull. Calcutta Math. Soc. MR 2392281 |
| Reference:
|
[2] Brown A., Halmos P. R.: Algebraic properties of Toeplitz operators.J. Reine Angew. Math. 213 (1964), 89–102. MR 0160136 |
| Reference:
|
[3] Halmos P. R.: Hilbert Space Problem Book.Springer Verlag, New York, Heidelberg-Berlin, 1979. |
| Reference:
|
[4] Ho M. C.: Properties of Slant Toeplitz operators.Indiana Univ. Math. J. 45 (1996), 843–862. Zbl 0880.47016, MR 1422109 |
| . |
