Fourier Analysis of a space of Hilbert-Schmidt operators: new "Ha-plitz" type operators
- Autores: Jaak Peetre
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 34, Nº 1, 1990, págs. 181-197
- Idioma: inglés
- DOI: 10.5565/publmat_34190_14
- Títulos paralelos:
- Análisis de Fourier de un espacio de operadores Hilbert-Shmidt: nuevos operadores tipo "Ha-plitz"
- Enlaces
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Resumen
If a group acts via unitary operators on a Hilbert space of functions then this group action extends in an obvious way to the space of Hilbert-Schmidt operators over the given Hilbert space. Even if the action on functions is irreducible, the action on H.-S. operators need not be irreducible. It is often of considerable interest to find out what the irreducible constituents are. Such an attitude has recently been advocated in the theory of "Ha-pliz" (Hankel + Toeplitz) operators. In this paper we solve this problem [for] the space of H.-S. operators over the Hilbert space L2(?, µa) of square integrable functions over the unit disk ? equipped with the Dzhrbashyan measure dµa(z) = (a + 1)(1 - |z|2)a dA(z) (a > -1). This complements the earlier results. In particular we discover many new Ha-plitz type operators. The question of their smoothness properties (Sp-estimates etc.) is however only touched upon.
