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Generalized Fock spaces, interpolation, multipliers, circle geometry.

Jaak Peetre, Sundaram Thangavelu, Nils-Olof Wallin (1996)

Revista Matemática Iberoamericana

By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e-Q(z), where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle C in C. We consider the problem of interpolation between two Fock spaces. If C0 and C1 are the corresponding circles, one is led to consider the pencil of circles generated by C0 and C1....

Generalized Lions-Peetre methods of constants and means and operator ideals.

Antonio Manzano, Mieczyslaw Mastylo (2007)

Collectanea Mathematica

We establish results on interpolation of Rosenthal operators, Banach-Saks operators, Asplund operators and weakly compact operators by means of generalized Lions-Peetre methods of constants and means. Applications are presented for the K-method space generated by the Calderón-Lozanovskii space parameters.

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