Fourier analysis of a space of Hilbert-Shmidt operators. New Ha-plitz type operators.

Título inglés	Fourier analysis of a space of Hilbert-Shmidt operators. New Ha-plitz type operators.
Título español	Análisis de Fourier de un espacio de operadores Hilbert-Shmidt. Nuevos operadores tipo Ha-plitz.
Autor/es	Peetre, Jaak
Organización	Mat. Inst. Stockholms Univ., Estocolmo, Suecia
Revista	0214-1493
Publicación	1990, 34 (1): 181-197, 16 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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(Δ, μα) of square integrable functions over the unit disk Δ equipped with the Dzhrbashyan measure dμα(z) = (α + 1)(1 - |z|2)α dA(z) (α > -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.
Clasificación UNESCO	120201
Palabras clave español	Operadores ; Operadores de Hilbert-Schmidt
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